You’ve sipped cocktails in Manhattan, been on the Staten Island Ferry, shopped till you dropped, travelled to the top of the Empire State Building and you’ve hung out in Greenwich Village; chances are you think you’ve done the Big Apple.

But have you really seen everything there is to see? Here’s our list of the top ten quirky, unique, out-of-the-way, unlikely and just plain odd outings and things to do that make any trip to the five boroughs, well worth your while.

1. Night court – Justice in New York is doled out 24 hours a day, seven days a week and proceedings are open to the public and that includes out of town-ers. You can watch thieves, hookers, drug dealers and petty criminals all be arraigned, with the average case taking just ten minutes.

The county court at 100 Centre Street in Lower Manhattan, deals with a variety of matters and characters from 5.30pm till 1am. Note that on arrival you and your belongings will be scanned by security, but tourists in the know use this as an opportunity to ask the guards which room is likely to have the most interesting cases. So if you’ve ever wanted to be part of a ‘Law and Order’ moment, this is one experience you shouldn’t miss.

2. Gracie Mansion – This grand house is the official residence of the mayor of New York and one of the city’s oldest surviving wooden structures. Built by Scottish shipping magnate Archibald Gracie in 1799, this two-storey manor has been lovingly restored and is used for official city business including civic receptions. If you’d like to see how the other half lives, you should take one of the guided tours, but be warned, you will need to book in advance.

Tours go for around 45 minutes and take in state rooms, gardens, the library, private apartments and much more. The views from the bedrooms upstairs overlook Hell’s Gate, which is taken from the Dutch phrase Hellegat which apparently means bright or beautiful passage. To book a tour visit nyc.gov and follow the links to the public tours page of the visitor section of this site.

3. Eldrige Street synagogue and museum – We Irish aren’t the only global community who have left our stamp on the city that doesn’t sleep, learn more about the Eastern European Jews who flocked to the Lower East side in the 1880s at this unique museum and house of worship.

Recently restored to its former glory, Eldrige Street was the first synagogue built in the US and the stunning architecture is a sight to behold. The museum offers walking tours in the summer which cover everything from Jewish dating rituals at the turn of the century to colourful Jewish figures from gangsters to writers. For times and fees, visit eldridgestreet.org.

4. Eat out for just $1 – The global financial crisis is clearly having an impact, with hipster rag Time Out naming the top ten bites that come in for around one buck. The good news is that among the fish dishes, tacos, Chinese dumplings, sodas and desserts is a $1 mini-burger courtesy of an Irish bar in Brooklyn called Cyprus Avenue.

Your friends may not believe it when you tell them that you ate out for $1, but your bank manager will thank you. Visit timeout.com for the full guide to where to go and what to eat for just $1.

5. Roosevelt Island Tramway – With a top speed of just 16 miles per hour, this is a unique way to get across the East River, but the spectacular views are among the best you will see in New York. It’s a visual wonder that is used by tourists and commuters alike to get from busy Manhattan to Roosevelt Island. And for just $2.25 each way or $4 return, it’s also not going to eat into your travel budget.

Please note though that the service will be suspended until the end of July 2010, so that work can be completed to modernize the tramway. So if you’re off to New York next week, this may be something to put on the to-do list for your next trip. For more up to date information, visit the tramway’s website at rioc.com .

6. PS 1 contemporary art museum – This museum bills itself as home of the most experimental art in the world. Founded in 1971, this space is the edgier sibling of the famous Museum of Modern Art.

You can see everything from tropical trees encased in concrete to installation pieces from a wide range of artists and Pole Dance, a courtyard of 25 interconnected bungees and poles that set off various sounds when touched or used by the public.

This is one gallery that will challenge your idea of what art truly is and leave you with plenty to think about. The museum operates walking tours which may help you navigate your way through the unique pieces that are on display. For more information, visit ps1.org.

7. Louis Armstrong House Museum – Jazz icon Louis Armstrong and his fourth wife Lucille purchased this unassuming Queens home in 1943, where they lived for the last 28 years of the great man’s life.

Curators have preserved the house so that it looks just as it did when Armstrong was alive. On a guided tour, visitors get a very intimate look at the world of one of America’s greatest musicians and his wife.

You can see everything from the couple’s vastly different taste in interiors, or listen to some of Armstrong’s home recordings, see memorabilia from his prolific career and in the den you can find the museum’s central asset – the great man’s large collection of reel-to-reel recordings of music and conversations with family and friends. There are also regular gigs and concerts held at the museum, particularly over the summer. For more information, visit louisarmstronghouse.org .

8. Grant’s Tomb – Completed in 1897, the General Grant National Memorial in Riverside Park is home to the remains of civil war icon Ulysses S Grant. The 18th President of the USA commanded the Union Army during the American civil war from 1864 to 1865. Twenty years later, more than one million people turned out for his funeral parade in 1885, which was 11 kilometres long and included both Union and Confederate generals.

Grant and his wife are buried in what is believed to be the biggest mausoleum in the US. Learn more about this man and the unique contribution he made to American history at this large national monument. Visit grantstomb.org for more information about the site’s opening hours.

9. Museum of sex – Probably not the place to buy postcards to send home, but this odd museum on Fifth Avenue is nothing if not informative. While there are many museums around the world dedicated to this subject matter, this is one run by academics who say they are keen to educate visitors on the history of human sexuality.

The museum is split into three spaces; one for temporary exhibitions, another for famous sex scenes on the big screen and a final display of 15,000 sexual artifacts. Be warned though that the hilarious, shocking and visually engaging material is clearly of a graphic nature. All entrants have their ID checked at the door to ensure that visitors are aged over 18. So if the very idea of this place turns your stomach, chances are you should give it a miss.

10. Forage food tours – Author of The Wild Vegetarian Cook Book Steve Brill shares his knowledge of edible wild foods and where you can find them in the city that never sleeps. He says he’s the man “who ate Central Park”. His forage tour includes wild plants as well as more obvious food sources such as mushrooms.

He attracts around 50 people at weekends to his park forage session, with many participants being vegetarians and vegans who are eager to learn more about how to source food from their local area. Identifying safe food sources is paramount and Steve will also show you ways to prepare and cook some of these unusual ingredients. .

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