The Bronx, beloved of TV cop shows and immigrants, but not the first place that leaps into the minds of tourists. Ask any of the 343,000 Irish visitors to New York last year why they were there, and you can be pretty sure that none said it was to see the Bronx.

Some might have expressed an interest in its trendier cousin Brooklyn (I can't see a celebrity couple naming their child 'Bronx Beckham') but the Bronx still hangs on to its Fort Apache/Bonfire of the Vanities reputation as a tough, crime-ridden no-go area. Of course, the hackneyed stereotype is wide of the mark. There is much to do and even more to see by crossing the river for a day or two in the course of a visit to Manhattan.

Just across the Harlem River, Riverdale is a good place to start for the Bronx novice. Take the uptown Number 1 or 9 subway train to the last stop at 242nd Street. Just before the train pulls into the station, keep an eye out for Gaelic Park, the fabled GAA ground in New York, which has been a sanctuary for Irish immigrants for almost a century.

When you leave the station you're on Broadway (despite being the quintessential Manhattan street, Broadway stretches all the way up from the southern tip of Manhattan to the Canadian border, though it's renamed Route 9 from Yonkers on), and if you're hungry check out the Short Stop diner at the entrance to the subway. Dingy looking on the outside, the breakfasts are delicious and great value.

Across the road is Van Cortlandt Park, which runs from here up to Yonkers. The fourth-largest park in New York City, it has a public swimming pool – bizarrely, considering that in can be in the 30s from May through to September, only open in July and August – a lake, running trails, baseball and football pitches, hurling, Gaelic and soccer for the Irish expats, and cricket for the Asians. On hot summer days, the local Hispanic families arrive early in the morning to get their spot in the shade, tying bunting to trees, lighting barbecues and laying out tables full of food and drink. Van Cortlandt is also home to America's oldest public golf course, where you can hire a set of clubs and play 18 holes for $60.

Heading east towards the Hudson River is Fieldston, one of the wealthiest areas in New York City. A neighbourhood of privately-owned streets, Fieldston consists of around 250 houses in a bizarre mixture of Tudor, Norman and medieval styles. Sniff the air and you can smell the money, with each house more grandiose and ostentatious than the next. The whole area has been "landmarked", the American equivalent of having a preservation order put on it.

A few more blocks east and overlooking the Hudson is Wave Hill, a 28-acre garden with two 19th century mansions, which were at one time home to, amongst others, Mark Twain and Teddy Roosevelt. (Wave Hill is said to have given Roosevelt his love of nature which resulted in him preserving millions of acres of American parkland when he was president.)

The gardens are fabulous, with 3,000 different plant species, woodland walks, shady pergolas and lots of places to sit and chill (or get married; it's a popular place to tie the knot). But what really takes your breath away are the views across the river to the Palisades in New Jersey. All you can see are trees and water. You almost expect to see Native Americans pedalling along in bark canoes. The only hint that you are actually in New York City is the top of the George Washington Bridge shimmering in the distance.

Leaving Wave Hill (for movie fans, the house opposite the entrance is where the external wedding scenes in The Godfather Part II were shot), you can either walk back to the subway, stopping at An Béal Bocht, an Irish café bar on West 238th Street, for some refreshments, or head down Palisade Avenue, past the 19th century manor houses which are like country estates, to the wonderfully named Spuyten Duyvil train station on the banks of the Harlem river, and in 20 minutes you'll be back in Grand Central Station. Alternatively, there is a free shuttle bus from Wave Hill to the metro station.

If it's more fauna than flora you're after, then Bronx Zoo is definitely worth a visit. The zoo is the main tourist attraction in the Bronx and probably the only reason that other New Yorkers visit the borough. As it's the largest metropolitan zoo in the US (256 acres; by comparison, Dublin Zoo is just over 60), it's worth spending a whole day there. There are over 4,000 animals (although in recent weeks the recession has hit the zoo and resulted in hundreds of animals being redeployed to other institutions) and a number of unique habitats, areas designed to replicate the homes of their inhabitants as closely as possible.

Jungle World, for instance, is an indoor rainforest where Asian gibbons, hornbills, tapirs, and many other rare species live among equally rare plants and trees. The zoo's newest exhibit, the Congo Gorilla Forest, features acres of shady forest, treetop lookouts, rock promontories, streams and wading pools, and bamboo thickets, all home to an amazing collection of animals, including two troupes of lowland gorillas.

Right next to the zoo there are more delights for the flora fan in the New York Botanical Gardens. Around the same size as the zoo, plant-lovers could spend hours, if not days, walking through the 47 gardens and 40-acre forest. (If you prefer your Botanical Gardens more manageable, then the one in Brooklyn is maybe worth a trip, especially in spring when the cherry blossom festival takes place; interestingly, the two gardens, though less than 20 miles apart, have very different climates.)

If all that walking has given you an appetite then head to nearby Arthur Avenue in Belmont. The original Little Italy, it also features in The Godfather, and is said to have the best Italian food this side of Tuscany, with loads of cafés, delis (the hot Italian sausage from Mike's Deli is particularly good), and one of the best Italian restaurants in New York, Roberto's, on Crescent Avenue, two blocks over from Arthur Avenue. You may have to queue for a table as they don't take reserva­tions but it's well worth it for dishes such as homemade pasta with cauliflower ($18) or grilled octopus with cannellini beans ($14).

And if none of the above tempt you to the Bronx maybe the mile-long Orchard beach, known as the Bronx Riviera, complete with boardwalk might do the trick.

Or City Island, a small community reminiscent of a New England fishing village, with boatyards, antique shops, art galleries and many, many seafood restaurants.

Or tree-lined Woodlawn Cemetery, the final home of, amongst others, Herman Melville, Duke Ellington and Miles Davis.

And you never know, you might even get a walk-on part in Criminal Minds.

Getting there

From Dublin and Shannon you can fly direct to New York JFK with Aer Lingus (aerlingus.com), American Airlines (american airlines.ie) and Delta (delta.com); Continental (continental.com) also flies from Dublin and Shannon to Newark in New Jersey. Around the same distance from the city as JFK, it's normally less crowded, and you get a great view of the Manhattan skyline as you're coming in to land. And if you really want to arrive in style (and get an even better view of the skyline) you can get a helicopter transfer from the airport into midtown Manhattan from $159 (flyush.com).

Staying there

The recently refurbished Irish-owned Fitzpatrick's Manhattan hotel on Lexington Avenue in midtown is a great place to stay. Its location, within walking distance of Central Park and the museums and galleries, and all the shops you could want (its two blocks down from Bloomingdales and round the corner from 5th?and Park Avenue), is such that you could spend an entire week there without needing to get on a subway or in a taxi. Check out fitzpatrickhotels.com/ manhattan for deals.

nycgo.com is the tourist destination website of NYC & Company; the New York City Tourist Board. The site is constantly updated with the very latest information about what is hot and happening Now in New York City.

Continental Airlines, voted Best Airline to North America by Irish travel-industry professionals in the 2009 ITTN Awards, operates non-stop flights from Dublin (twice daily), Shannon and Belfast (both daily) to its New York hub, Newark Liberty International Airport, with onward connections to over 200 destinations throughout the Americas. For reservations, call Continental on 1890 925 252 or visit continental.com.

The Fitzpatrick Hotel Group New York offers deluxe accommodation in the heart of midtown Manhattan, with a choice of the Fitzpatrick Grand Central and the newly redesigned Fitzpatrick Manhattan. www.fitzpatrickhotels.com