Serious food in Providence, on a budget
I'm headed from NYC to Providence next week to visit a friend. She's a grad student, and I'm temporarily unemployed (or as I prefer to say, on sabbatical).
We love to eat. Ambience not necessary; chairs are optional. All cuisines.
Taqueria Pacifica in AS220 has damn good So Cal Tex Mex and a nice selection of beers in a funky atmosphere at cheap prices.
Chilangos on Manton Ave is probably the best Mexican food in the city, and they even have chairs! There are cheaper taquerias, but I think Chilangos is well worth the extra buck or so, and still plenty cheap.
There are numerous Asian restaurants that are quite inexpensive in the elmwood area, the most reknowned of which is Apsara (not to be confused with the Apsara Palace on Hope St, which is unrelated. Apsara's portions are huge, so you could certainly split a starter and a main and be full.
Just want to second Taqueria Pacifica - delicious, fresh, and definitely in your budget.
I'd also recommend Nick's on Broadway for breakfast or lunch. They just recently started dinner service, but I don't know if it would be out of your budget (haven't checked it out yet).
If you do a web search, it will say that they're at 259 Broadway. But they recently moved up the street - into the 500's - but I don't know the exact street number.
Finally, Bob & Timmy's makes a great RI-style grilled pizza - I would recommend anything with their mixed grilled mushrooms. Yum.