there is this Hamburger joint in Harvard Square we loved it when we visited Boston a couple of years ago.
Was it one of these:https://www.charlieskitchen.comhttps://www.mrbartley.com
Both great and have been there for years. I was in school there in the early 70s, and they are still great as they were then.
Charlies Kitchen has really cheap beer and food, always has.
Monkhouse, as one of the posters said, take the T as a great cheap transportation option, that's great advice. Harvard Square and Harvard have a lot to offer for really cheap, including free tours.