All the details below not just MHO, we got all the details from tripadvisor.co.uk prior to our trip and they all lived up to (and exceeded the hype - Most of the pointers come from people resident in NYC)
Eats -
Try Grimaldi's for Pizza
> Over the Brooklyn Bridge by the promenade
> Then stroll back over the bridge to Manhattan afterwards
> Voted one of the best two Pizza places in NYC (other being Lombardi's).
Katz Deli
> 205 East Houston Street (Lower East Side)
> A New York institution! - Best pastrami or corned beef on rye in Manhattan
> Meg Ryan enjoyed it in 'that' film

Juniors @ Grand Central
> Best cheesecake in the world - never mind NYC
> Grab a slice to take away and enjoy back in the hotel with a coffee........or even a beer
Shopping -
> Look out for 'Yellow Rat Bastard' stores
> Great T-shirts / Jeans etc
Bars -
> So many! Didn't find a bad one in our time there
Music -
> CBGB's - Still alive and well at 315 Bowery
> The place that launched the Ramones / Talking Heads / Richard Hell etc etc
Overrated -
Century 21
> Huge crowds, suffered 10 minutes of the place before calling it a day
Times Square
> Visit it during the day and night......but don't eat or drink there
much better places downtown
Different things to do -
> Catch the subway down to Coney Island and walk along to Brighton Beach (re-living 'The Warriors' on the way [y]
> Loads of bars and a thriving Russian community
Have fun