If you do a search in the group for the month you're looking to move e.g. June sublet you should be able to see all the options available in that group. Unfortunately, anything below $2k for an entire place is likely to disappear fast, you'd have better luck if you get comfortable with spending between $2.5-$3k/month.

Kendall, but there's only one grocery store there called Roche Brothers that's stupidly expensive (it's still mostly office buildings and nice restaurants in that area). But for an intern with an unlimited budget, it'll do. It's pretty quiet area too.

Central is buzzing with a lot more casual restaurants, clubs, and shops and it's next to Kendall. Central has a Whole Foods and an HMart (big Asian grocery store chain). A lot of MIT and Harvard students seem to live around there, the nightlife is pretty good.

Have you joined the MIT/Harvard housing groups on Facebook? Would recommend that, lots of people trying to sublet their places on there. For a one bedroom, you are most likely looking at $1.9k-$2k+ per month, anything below that is probably a scam.