I lived on 66th/1st for about 8 years until I moved last summer. Here were my standbys:
Meditarreneo and it's sister restaurant ZaZa - pretty good all-around italian (no pizza at ZaZa), very friendly staff. Meditarreneo is definitely more of a "scene" - corner of 66th/1st Ave. ZaZa is much quieter but there's almost never a wait for a table - 1st Ave/65th St.
Afgan Kebab House - really delicious kebabs (naturally) but also great apps and the best rice pilaf ever! Also very friendly. BYOB. 2nd Ave/70th St.
Becky's - mellow neighborhood pub with surprisingly good burgers. Some nights lively, some nights totally dead (which was not a bad thing). 1st Ave/63rd St.
Bagel Works - really awesome NYC bagels and spreads, made fresh daily. Line goes out the door many mornings. 1st Ave/66th St.
Maya - gourmet Mexican, chef is Richard Sandoval who owns many other great restaurants in NYC. 1st Ave/64th.
Cafe Evergreen - agree with previous post, really excellent dim sum Sunday mornings. Better than many places in Chinatown. Other food is okay.
Tsuki - authentic sushi, fresh and abundant fish choices, great sakes. 1st Ave/74th St.
1288 1st Ave, New York, NY 10021
1410 1st Ave, New York, NY 10021