Ok so, I hope I'm not overstepping my bounds here as this is my first post but I want to throw some facts at you.
Copley is very nice, and would be a sweet place to stay; however, you're looking at some jacked up hotel prices. A much much better idea would be to stay somewhere in Newton. The Sheraton over the pike in Newton Corner is very convenient but since it's over the pike, it might be kind of loud. Another choice is to stay at the hotel right next to the Riverside T stop. It may be at the very end of the green line but it's in Newton, it's literally 500 feet from a stop, and it's ridiculously cheap; AND since it's at the very end of the line, almost every single stop up until the Fenway stop is pretty uncrowded and easy going.
As for going to Salem, there is a ferry that heads there and they've got plenty of bikes or mopeds if you're into that thing. The same goes for Martha's Vineyard/Nantucket/most other places on the Cape. If you want to save some cash, the ferry is much cheaper than a rental car and you won't have to drive around with us Massholes.
The foliage IS gorgeous and it's highly recommended to get a car for a day and drive out as far west as you can. Not necessarily all the way to Amherst but halfway there it becomes less cityish (nothing is grosser than driving through a crappy town like Saugus) and more rural with beautiful trees and fields.
Fun touristy things to do are Fenway Park (expensive), checking out the Zakim bridge at night (gorgeous), the science museum, the aquarium, the freedom trail, Copley and the Prudential for shopping, old north church, the north end for overpriced Italian food (that's one of those places that is overhyped but you still have to go there), and grab some seafood in the harbor (No Names is a pretty popular destination for tourists.) There's also Fanueil Hall (which I'll never spell right) and the surrounding area.
Like I said, all of those are pretty touristy but all my visiting friends seem to enjoy it. For the non-touristy things, there's Church (bar, not actual church) in Back Bay and Jim's Deli in Brighton. Both of which are wicked easy to get to via T or bus.
Anyway, hope I could help and enjoy Boston (PS: If you're on the T, and you're not sure it's your stop but you stand in front of the door anyway, you WILL get pushed the hell off
PPS: If you see a "roundabout" or "rotary" in Boston.. then you're not in Boston. You're probably in Roslindale or JP or Hyde Park or something.