If you're on a tight budget in NYC you should be macking on the student crowd. The good news is that the East Village is a student hotspot!
Get yourself a burrito at Downtown Bakery - it's legit, and cheap -
http://www.yelp.co.uk/biz/downtown-bakery-new-york
There's a cheap falafel spot on St Mark's, something like two pittas for $5.
Opposite the Ukrainian church there's a basement that serves really cheap borscht and other Ukrainian specialties a few nights a week. It's served up by cheerful old Ukrainian ladies. It's called Streecha I think.
East Village is dive bar central. Plenty of cheap bars catering to the college crowd. I was off my head last time I went there, but the 13th Step on 2nd around 9th is often buzzing. They do promotions such as $1 for a beer on certain nights. Don't remember much about the crowd. There are similar places along St Mark's, often with plenty of students. Not the best talent though.
A short walk to the West you have the Fat Cat - again cheap beers and plenty of NYU college crowd action -
http://www.yelp.co.uk/biz/fat-cat-new-york-2
For a more clubby vibe there's Lit Lounge on 2nd ave between 5th and 6th. Plenty of fashion girls and model types come here and it's not too expensive -
http://www.yelp.co.uk/biz/lit-lounge-new-york
For top talent (as of a couple of years ago at least) hit up the Blind Barber on 10th between A and B. It's a speakeasy but cheaper and less pretentious than most (read: Crif Dogs / PDT, also in the EV but expensive). Entrance is through a barber shop but it's obvious that there's club action going on there. Entry is free, but they sometimes run a tight ship on the door so be well-dressed and don't roll with a group of guys.
If you're really on a budget why not pregame at home and then go easy on buying drinks. You'll get better mileage than restricting yourself to only places with cheap drinks. Check out my NY datasheet.
Only bad thing about the EV is that you can go out every night till 5am easily. Half the fun of that part of town is walking around, exploring, talking to people and getting their tips.
And once you've done the rounds drop us an East Village datasheet!!