Maybe Republic Noodles?
37 Union Sq. (btw 16th & 17th st.)
You will feel like you are in the middle of Web hall, already.
Or, really, you could search for East Village recs in general.
Crif Dogs 113 St. Marks Pl (Btw 1st ave & A) would be a schlep but fun.
Rai Rai Ken. 10th btwn 1st and 2nd. Ramen, have heard mixed things about it.
Minca. 536 E 5th St (btw A & B) Ramen, have tried this one and liked it, take a bus from union sq.
Paul's Place. 131 2nd Ave (at St. Marks Place). Burger place I've been meaning to try, people say nice things about it.
(Have fun, don't forget to wear earplugs.)