There's plenty to do in New York.
I dunno what that other graffiti suggestion was but if you're really into that sort of thing, check out the Freedom Tunnel which runs from 125th St. to Midtown under Riverside Park. The grates from the park illuminate large alcoves in the walls; this creates what is essentially a natural gallery space and has made the place an attractive display area for street artists. The work on display there generally goes above and beyond your typical street tagging, ranging from murals depicting the eviction of the mole people (when the tunnel originally fell out of use by Amtrak, shanty towns sprung up inside and flourished for years. When Amtrak decided to use the tunnel again, they bulldozed the shanty towns and kicked out arrested all the homeless. Evidence of their lives, everything from school bags to novels to cheese graters, and in one spacious area even an electric chandelier, still lies scattered on the ground) to a chiaroscuro study of the Venus de Milo. Even a recreation of Goya's "The Third of May".
Mind you, this is an active train tunnel on private property owned by Amtrak, and if you're caught there you're in danger of receiving a trespassing charge. The tunnel houses two tracks in opposite directions but is approximately four tracks wide, leaving of plenty of room for humans. It's 99% safe as long as you are mindful of your surroundings (the ground is covered in debris from the bulldozed shanty towns) and duck into the cover of darkness when you hear a train coming (they come approximately every half hour and make a loud honking noise that is heard at least 20 seconds before they appear). My friend and I have led three expeditions down there so far and have never been caught, nor have ever encountered another living soul save the passengers/conductor on the passing trains. We did once make enough noise to attract the attention of a small child above ground in Riverside Park who followed us for ~15 minutes, trying to peek through the grates.
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There's also plenty of dives, some cute cafes, and some fantastic restaurants that I can suggest if that's the kind of thing you want. Lots of live music and street entertainment if you steer clear of the touristy areas (Times Square, Midtown, though the latter is nice to walk through during the Holiday season to look at the decorations).
Places you generally can't go wrong with and shouldn't miss:
Beard Papa's - amazingly delicious cream puffs in various flavors. (There's four here, one on Astor Place in the East Village, one in the West Village, one in Midtown, and one on the Upper West Side)
L'Arte Del Gelato - fantastic Italian-style gelato, which could unjustly be compared to American ice cream. Don't be tempted by any of the other gourmet ice cream shops located steps away from their Bleecker St. location. This one is by far the best. (There are three, one inside the Chelsea Market (a delicious destination in and of itself, it houses plenty of gourmet shops as well as the Food Network's main studio where they shoot Iron Chef America and a bunch of other crap), one on 7th Ave. between Bleecker St. and West 4th, and one in Lincoln Center (home of the Metropolitan Opera, the New York Philharmonic, and the American Ballet Theatre as well as a massive private library of media open to the public and the famed Julliard School) closer to Midtown).
Le Petit Belge - delicious Belgian waffles served with a variety of toppings. There isn't much indoor seating. The place is a high-class hole in the wall, but the dessert is totally worth it. (As far as I know, there is only one, by Union Square on East 14th St.)
Pommes Frites - authentic Belgian frites and myriad sauces to go along with them. Ketchup here is a crime though they will oblige if you ask. This is also a hole in the wall, considerably less high class but cozy and inviting nonetheless. If you manage to grab a seat in the back, that is. If you don't, they serve their frites in heaping portions inside large paper cones, so you'll be fine walking down the street with one. (There is only one, in the famed "birthplace of bohemia/punk rock mecca yada yada St. Mark's Place)
Max Brenner's - chocolate heaven. If you like dessert, you must go here. Ignore the shitty review, that guy knows not what he's talking about. (I'd suggest the one in Union Square over the address listed there. It's larger yet cozier.)
Slightly more out of the way destinations:
Amy Ruth's - best fried chicken and waffles you will ever have. More worth the subway ride to Harlem than I can ever describe in words. Have the first thing on the menu- the classic fried chicken and waffles, though you can't go wrong with anything.
Dinosaur BBQ - totally fucking authentic barbecue, despite being quite a distance from the BBQ Belt (the American Southwest and parts of the Southeast where barbecue is not so much a food but a way of life). This one's also in Harlem, same trip but completely worth it.
West Harlem in general is not a bad place! The Apollo Theatre, the presence of Columbia University and Columbia Presbyterian Hospital, and the remnants of the Harlem Renaissance have kept it a safe and colorful, if not wealthy, neighborhood. Just don't stray into East Harlem, which is pretty slummy.
Shit, this post took about an hour so I hope it's at least somewhat useful to you.
Good luck and enjoy your trip!