Do the Empire State, for a laugh.
Walk everywhere as the metro system can be a little confusing due to multiple trains running on the same lines - i.e. you can have express trains that only stop every half a dozen stations or so, which can make getitng around a bit messy. If you stay south of Central Park, Manhattan is actually only about 2.5 by 1.5 miles or thereabouts - and it's pretty much a toast rack configuration above the financial district - i.e. Avenues run North South and numbered roads bisect them East to West - it's piss easy to find your way around.
Go ice skating in Central PArk
Go have a look at the Chelsea Hotel - I actually stayed there when I was there last, but it is a bit of a dump, but very trendy - it's on 23rd and 8th Ave. There are some excellent resaurants on 8th Ave, but it's very gay around there - I made the mistake of walking into a Big Cup coffee house one morning with the worst hangover and almost got eaten alive
Times Sq isn't a Sq as such and you'll almost certainly walk through it going, ooh pretty lights, but that's it.
Do 5th Ave/Broadway (Broadway IS 5th Avenue) to have a look at the lights.
The trendy bars are south of Houston (pronounced House Ton), hence the area being called SoHo. Bear in mind that New Yorkers go out and stay out late, so take some stims with you - basically most decent bars are quiet before 10pm, so eat about 8:30 - 9pm then go out after that - the bars don't really get going until about 11pm, but it's worth persevering as the night life is excellent and New Yorkers tend to be friendly if a little honest. Be polite to the bar staff and tip a buck or two on every drink and you should get every 4th or 5th free.
I'm not much for tourist stuff though, but if you enjoy shopping and chilling in bars you'll love NYC. Oh, yeah, go see Grand Central as well, that's a fantastic building.
There's a tangible energy about the place which will either float your boat or wear you out. It is very safe and clean, so don't worry about wandering around late at night or in the early hours - I regularly got back to my hotel at 5am by walking.
There is NO legroom in the back of those HUGE yellow cabs.
Enjoy it, it's a fantastic city