I'd say Chestnut Hill/Brighton. Brookline if you don't bring your car or can afford to park privately (no overnight street parking). It's a versatile location--you can be bougie in Brookline, party in Allston, or be whatever I am in Brighton. Green line will take you downtown (maybe even this century) and you can catch a bus to Cambridge.

You could go further out and get a bit more house. But it's still expensive and then you have to drive around a lot more. Not worth it. But maybe I'm biased. Just remember that driving and parking here really blows, and I learned to drive around LA and spent time in DC.

In terms of stuff to do, it depends what you enjoy! I recommend doing the touristy stuff across the city (Fenway, Boston Common, the library, freedom trail, museums, acquarium, zoo, all the stuff you see online). Take your time with it. Go out for drinks and food.

More locally, tons of good food of all kinds. Publick House in Brookline, Tasca, Cafè Landwer, Moogy's. Many local bars, like Harry's or the Ave. Maybe pass on the Silhouette, but hey you do you. Again, just take your time.

Go walk around the Chestnut Hill Reservoir and visit the Waterworks Museum. Coolidge Corner Theater does these awesome "After Midnight" showings. For the silent films, they often get live accompanyment, which cna be awesome.