I saw your post a while ago, but my mind was a bit overwhelmed with all the possibilities, so I decided to give it a bit of a think.
Anyway, you should first check out the listings on this site for Massachusetts. The Sterns have reviewed a plethora of places north of the city and I would concur with their recommendations. I'm not real familiar with the northern reaches of our Commonwealth, but the Sterns are, so heed their advice!
Besides those, I guess it's hard to respond because there are so many diverse choices in and around the city and beyond. I'll tell you about some of my favorites.
In the South End of Boston, there's a place called the Delux Cafe (100 Chandler Street), which is a neighborhood joint, but very funky and great food. Loads of velvet Elvis paintings and everything is $10 and under. Also in the South End is Tim's Tavern (329 Columbus Avenue), where big and cheap hamburgers rule.
Let's see...outside of the city...heading towards metrowest, there's a great chinese noodle shop on Route 9 in Framingham called EO Noodle. It's been our Friday night staple for about 8 years now. Good homemade wontons, steamed raviolis and noodle soups. Don't leave without trying the scallion pancakes. The two of us can eat well there for under $20. There's no liquor license, though, but you can BYOB.
In Sherborn on Route 27, there is a little ice cream/burger stand called C & L Frosty. They have nice small, but fresh and handformed burgers, as well as some pretty good fried seafood. Get the hamburger (or cheeseburger) platter and you get two burgers, which solves the size issue!
If you want to head waaay west, there's loads of great diners in and around Worcester, starting with the old favorite, the Boulevard on Shrewsbury Street, which is open late for your post-partying hunger. Right across the street is the Parkway Diner, which has the best (or maybe second best) meatballs in town. They are not open late, but go for breakfast and get a meatball omelette. Oh yeah!
If fancy pastries are your craving, then head out to Medfield. Off of Route 109, take Park Street and there's a great bakery there called Dessertworks, run by my friends Leonardo and Kristen. A must have is their homemade "pop tarts." This is what a pop-tart should be! Flaky, buttery beyond belief and filled with homemade fruit preserves. They make some great cakes, too.
Well, those are my absolute favorites. Have fun!