Lima Cafe is a nice small 100% vegan restaurant near Shinjuku station (5-7 minutes from South Exit). The menu is not very extensive (3 or 4 main dishes and several desserts) and portions are a bit small but the food is tasty and worth its price (600-800 yen). There is also a health food shop in the same building that sells vegan lunch boxes (600yen), snacks and other tasty things for those who are still hungry ;-)
Update: after the increase in taxes from April 1st, all main dishes cost 900 yen which puts Lima in "medium" price range.
Cons: No English, Portions could be bigger