Capital one Cafes are always a good option for restrooms too, there's a few throughout the Boston area!

I think that under $2000 for a studio is going to be quite difficult to find in Cambridge. I paid about $1500 for a studio in Cambridge 6 years ago and that was MIT-subsidized housing (for grad students, unfortunately I don't think they have anything for postdocs). I think finding a cheaper 2 bed is significantly more do-able (could be easily <$1500/person). That being said, there are always occasionally random deals that pop up, but they'll often get snapped up extremely quickly. Places to look include East Cambridge and Alewife, also try looking in Somerville and if you're okay with a longer commute maybe look in like Allston or Dorchester/Roxbury? I know some folks who live there who have insanely cheap (to me as someone who lives in Cambridge) rent.

The Helmand (Afghan food) in Kendall has a private room and the food is great! I went to a group dinner of around 15 people there recently and I think it ended up close to 100pp with food and drinks

Was going to say this place! It's absolutely lovely and Stowe itself is such a great place to visit!

If you can get someone to let you into MIT's green building (it's the super tall one with the ball thing on top) there are views from many classrooms etc on the upper floors. Technically not open to the public anymore since Covid but no one with care.