Do not get a car. Uber or subway. Trust me.
Areas for food / going out
Rooftops:
-Mr. Purple @ Indigo (Lower East Side)
-Le Bain @ The Standard (Meatpacking District)
-The Jimmy @ James Hotel (Tribeca)
-PhD @ Dream Hotel (Meatpacking, not really a rooftop but its cool on Saturday evenings if you can get in)
Brunch:
-Jack's Wife Freda
-L'Artusi
-Bubby's
-Clinton street bakery
-The Cookshop
-Locanda Verde
-Bagatelle (if you're looking for a party brunch on Saturday/Sunday)
Areas in General:
- Lower East Side (cool rooftop called Mr. Purple @ Indigo, random hole in the wall spots, its kinda young on the weekends and crowded...particularly around )
-Meatpacking District (if you like clubs)
-West Village (good bars and restaurants)
You might want to check out La Marina, Sylvia's, Red Rooster, Harlem Tavern, Amy Ruth's in Harlem.
Can give you more if you need