A hotel in Boston is going to be more expensive than in the burbs. Still since you're getting in kind of late on the 2nd, I'd pick one along the river for the nice views. Those are actually in Cambridge. The Royal Sonesta comes to mind or the Embassy Guest Suites. Perhaps those are less expensive. That one is on the Boston side and it's kind of stuck out there by the road but the views would be lovely. There's a free rehearsal for the annual 4th of July concert on the Esplanade (I think) on the 3rd. It might be worth googling that if that event holds any interest.
I'd head out towards Northhampton for the evening of the 3rd if you want to get a less expensive hotel. It's about an hour drive, maybe more, from Boston proper. If you're a knitter though, you really should check out Webs in Northhampton (http://www.yarn.com) great website but and even better store. It's outstanding. I actually make the drive out there 1-2 times a year just to go that store. It's knitters' heaven. I'm sure it won't be open on the 4th but maybe the 5th.