If you area active, I'd suggest waiting till after dark and then running over the Brooklyn Bridge. If you want a pretty good/tough run (I love it at night) the BMW run is good (Brooklyn-Manhattan-Williamsburg bridges). I can map it out if you are at all interested. The city looks amazing from the bridges at night.
I second the suggestion of Riverside Park. Just stay below 125th st. While up there you can check out Riverside Church and Grant's Tomb.
The loop in Prospect Park is also nice (Brooklyn). Van Cortlandt Park is THE place to run XC in NYC. Many, many famous runners have pounded the trails out there.
We have a saturday run out of Niketown (57th btwn 5th & Madison) that leaves at 9:30 am. It'll be an organized run through central park. I'm only in charge of the weekday runs, but the store organizes the saturday runs. They have bag check, shoe trials, & post run refreshments.
as far as bars, its tough to make suggestions b/c I don't know what you like. I tend to end up at lounges and dive bars. I hate clubs and trendy type places.
i do like this place:
http://www.bar89.com/. Coolest bathrooms in NYC. Decent food, cool place. I'd suggest making reservations.
My favorite restaurant in the city is
http://www.kumainn.com/. Get the Edamame. Get the garlic rice. The baby octopus is good as well. You'll need reservations. They are closed on mondays. You'll miss the place if you don't know its there....its upstairs and TINY It's byob, so grab a bottle of wine.
If you like live music, stop in Rockwood Music Hall on Allen btwn Houston and Stanton after dinner at kuma inn. Tiny little place that has amazing sound. Artists like Ryan Adams, The Killers, Norah Jones, etc have stopped in and played surprise sets. If whoever is playing isn't that great, move to the back room and sit in the movie theater seats at the table by the window and people watch.
I'm not sure when Luna Park (in Union Square) opens back up, but if its open, its a great place to have drinks outside. Also, check out the boat basin for outside drinks.
I'm a sucker for the Bronx Zoo. Worth a trip up there if you have the time.
Coney Island is kind of crappy, but can still be fun. Although it would be a little early in the season for that.
The Staten Island Ferry is free and will get you close enough to the statue of liberty if you don't want to wait in line for hours for the tour boats. Just get right back on the ferry b/c there isn't anything on SI worth staying for.
that's a start...give me more info on what you like to do and what kind of places you would typically hang out at and I can probably give you more info.
[This message has been edited by AggieOO (edited 4/3/2009 3:21p).]