The Union's most densely populated state is also pleasantly rural. But thrill-seekers need not flee to New York: there are casinos, shops and chic hotels galore.

Why would I go there?

If you fly to New York from the UK there is a good chance that you will be going there anyway: Newark airport is New Jersey's main entry point. Most people head east across the Hudson river as soon as they land, but according to one local resident, John Parker, who works for the state park service, the state of New Jersey has plenty to invite people to stay: "It's an all-round state. We have swimming, fishing, skiing; there are casinos, and it's between New York and Philadelphia, which makes it very convenient." Add to this some long-established seaside resorts and one of oldest university towns in the country. Although it is the most densely populated state in the Union, much of New Jersey is also unexpectedly rural.

Surprise me

Most visitors are attracted to the Jersey shore: 127 miles of Atlantic coast with a mixture of lively resorts and sandy beaches. Most northerly is Sandy Hook, popular with city dwellers wanting a day by the sea. Here you can swim with a view of the New York skyline in the background. Towns were settled by various different groups, giving many of the locations an individual character. Ocean City, for example, was settled by Methodists and it has remained a town where sales of alcohol are prohibited (although the official spin is that it is a "family resort").

Barrier islands, including the Barnegat Peninsula, shelter much of the mainland shore. At the southern end of the peninsula is Island Beach State Park, a protected area of dunes and marshes with a number of bird colonies. There are no amenities but it is a lovely spot for swimming and hiking. Admission costs $5 (£3.30).

There is a charge to use most of New Jersey's beaches during the summer season, which extends from late May to Labour Day in early September; beach tags are usually available from kiosks on the shore. There is no charge at Atlantic City or the Wildwoods, a group of beaches down on Cape May. Many of the resorts are seasonal and outside summer pretty much everything closes down. But Cape May, at the southernmost tip of the state, is a year-round destination.

What will I find there?

New Jersey's oldest seaside resort is one of the most delightful spots on the eastern seaboard. It's a charming Victorian town with a historic district full of beautifully restored houses built in the 19th century, when this was the place to spend the summer. According to John Rogers, who has lived in Cape May for 32 years, what makes the place different from others on the coast is its atmosphere. "The people are so friendly," he says, "and there is a small-town feeling. It's the quaintness of the town that really makes it different." And he recommends the beach, as well as the town itself. "Enjoy the ocean – don't take it for granted."

Cape May is easy to walk around, but a good way to view the houses is to take one of the trolley tours that depart regularly from the information kiosk at the end of Washington Street Mall in the town centre (001 609 884 5404; capemaymac.org ), and which cost $10 (£6.60). A variety of architectural styles, from Carpenter's Gothic to Colonial Revival, is on display. Many of the buildings have wrap-around verandas, designed so that the inhabitants could show off their guests to the outside world. Others had bathrooms added to the side of the house and built on stilts, a sign of one-upmanship that was sure to impress the Victorian neighbours. One of the largest houses, the Emlen Physick Estate (capemaymac.org ) at 1048 Washington Street, has been turned into a museum and is open for tours, which cost $10 (£6.60) per person.

What about something bigger?

Another year-round resort, Atlantic City, is different from everywhere else on the Jersey shore. Like Cape May, it started out as a seaside resort. It became renowned for its boardwalk, a four-mile wooden walkway above the beach built so that visitors could enjoy the sand without trailing it into hotels and railroad cars afterwards. Atlantic City is the home of sand sculptures and a chewy confection known as salt-water taffy. (What's more, the original game of Monopoly was based on Atlantic City's streets.) But its reputation changed in 1976 when gambling was legalised, allowing the city to turn into a kind of Vegas-on-Sea.

Almost every big hotel in town has a casino, although it is perhaps more accurate to say that every large casino has a hotel attached. Gambling is the main activity here, and even if you don't play the tables it is impossible not to have your senses bombarded by the noise and lights of thousands of slot machines.

Kevin Hall is a native of Atlantic City and knows all the casinos. "The Borgata has a new, young, retro feel," he says; this one of several casinos located on the bay rather than the boardwalk (1 Borgata Way; 001 609 317 1000; theborgata.com ).

A jitney service – a kind of cross between a taxi and a bus – operates 24-hours a day up and down Pacific Avenue, linking the casinos for a one-way fare of $2.25 (£1.50). An alternative form of transport is the rolling chairs. These are, as the name suggests, two-seater chairs on wheels that are pushed along the boardwalk for a negotiable fee.

For anyone looking to spend their winnings, the best boardwalk shopping area is the Pier Shops at Caesar's – two floors of upmarket retail outlets, including Tiffanys, Coach, Gucci and Burberry, as well as more affordable stores such as Banana Republic and Levi's.

Anything more cultural?

Another of New Jersey's must-see destinations is Princeton, a small town that is the home of one of the oldest universities in America. Founded in 1746, its attractive campus spreads south from the town's main thoroughfare, Nassau Street. The colleges and faculty buildings are mainly Gothic in style, built around a series of courtyards and quadrangles; the whole area is lovely to wander around. There is also a large university chapel, with richly coloured stained glass, where concerts are often held. Like many university towns, Princeton has a good selection of cafés and restaurants, as well as several good bookshops including Labyrinth Books (001 609 497 1600;u olabyrinthbooks.com ) at 122 Nassau Street. Nearby, at the back of Landau's wool shop (landauprinceton.com), is an exhibition of photographs commemorating one of Princeton's most illustrious former residents, Albert Einstein.

Where can I stay?

Some of the most attractive accommodation in the state is in Cape May, where many of the Victorian homes have been turned into upmarket B&Bs, with comfortable accommodation in elegantly furnished rooms. These can be booked through Cape May Lodging (001 609 884 0080; capemaylodging.com ). However, the best hotel in the town is Congress Hall at 251 Beach Avenue (001 888 944 1816; congresshall.com ), which has doubles from $160 (£106). It started life as a boarding house for early seaside visitors; now it is a stylish hotel with luxury facilities.

In Atlantic City, the new Chelsea Hotel, at 111 South Chelsea Avenue (thechelsea-ac.com ) boasts that it is the first non-gaming hotel to open in the town for 50 years. It offers elegant boutique-style accommodation from around $250 (£167) per double; a new salt-water spa will be opening in April. Another stylish offering is the W, which is opening in Frank Sinatra's hometown, Hoboken, in February (starwoodhotels.com ). Campsites and cabins feature in several of New Jersey's parks and forests (njparksandforests.org ), including Bass River State Forest and Allaire State Park.

Inland highlights?

Most of the west side of New Jersey is bordered by the Delaware River, which divides the state from neighbouring Pennsylvania. There are some charming towns along the river, including Frenchtown, Stockton and Lambertville. These once industrial places have now been gentrified; many of the former factory workers' houses have been turned into gallery space for the artists, jewellery makers and antiques stores that have moved into the area.

A stretch of canal runs alongside the river, and beside it, in Lambertville, is an old railway building that has been converted to a restaurant with comfortable accommodation attached. The Inn at Lambertville Station is at 11 Bridge Street (001 609 397 4400; lambertvillestation.com ), and offers double rooms from $160 (£107), including breakfast.

Further north is a stretch of river known as the Delaware Water Gap, an area of stunning scenery that is popular for hiking and water sports. Beside it are the Kittatinny Mountains and High Point State Park, which has a cross-country ski area based at Lake Marcia (001 973 702 1222; njparksandforests.org ) as well as a 70-mile stretch of the Appalachian Trail, which links Georgia with Maine.

Wharton State Forest, in a flat, sandy part in the south of the state known as the Pine Barrens, has its own hiking route, the Batona Trail, which cuts through beautiful wilderness renowned for its flowers and birds. This area was once part of the industrial heartland of New Jersey; iron, and later glass, were produced here, and it was an important supplier of munitions during the Revolutionary War.

All that remains of that time is Batsto Village, a historic site where many of the old buildings, including the mansion house, general store, mills and barns, have been preserved. The grounds of Batsto Village (001 609 561 3262; batstovillage.org ) are open from dawn till dusk daily; the Visitor Centre opens 9am-4.30pm daily. A $5 (£3.30) parking fee applies in summer.

The writer travelled with British Airways (0844 493 0787; ba.com ), which offers daily flights from London Heathrow to Newark.

At liberty to shop

Population 8.5 million Area The size of Wales Capital TrentonDate in Union 18 December 1787 Flower Violet Motto "Libery and prosperity" Nickname Garden State

Land of the free

Two of the major attractions usually associated with Manhattan are easily reached from New Jersey – the Statue of Liberty and Ellis Island, where many of the nation's immigrants arrived, and which now houses a fascinating museum. Boats to both attractions depart from the old railroad station at Liberty Park.

Shop till you drop?

If you want clothes, New Jersey is the place to come, because no sales tax is levied on anything classed as a "necessity". There are outlet stores all over the state, including at Jersey Gardens in Elizabeth (jerseygardens.com ), where there are 200 shops under one roof.

Handy for Newark airport is the mall at Short Hills (shopshorthills.com ), whose department stores include Bloomingdale's, Macy's and Saks Fifth Avenue. It is only a few miles from the airport, so keen shoppers might consider a late shopping blitz before flying out.