My favorite in that area is actually right there: Mexicana Mama on 12th just west of Broadway. Specials are usually the way to go.
Una Pizzeria Napoletana (great Neopolitan pizza) on 12th btwn 1st & 2nd Ave
Otto (Italian/pizza) on 8th St just east of 5th Ave
Grand Sichuan St. Marks (Chinese) on St. Marks just east of 3rd Ave
Klong (Thai) on St. Marks just east of 3rd Ave
Hasaki (sushi) on 9th just east of 3rd Ave
Kanoyama (sushi) on 2nd Ave at 11th St
I would avoid the places on University Place.
1 5th ave at 8th st
30 e. 13th btwn 5th and university
48 e. 12th btwn university and broadway
105 w. 13th st at 6th ave
72 university pl btwn 10th and 11th st
80 university place at 11th
33 university pl at 9th