I wouldn't automatically discount Quincy because it is T-accessible and pretty close to Boston, but I would not stay at that hotel. It seems to attract the wrong element. If you want to stay on the outskirts I would check the Hyatt Place in Braintree, Holiday Inn, Braintree or the Marriott in Quincy. I would think both have free shuttles to the T. Avoid the lower tier motels. Another option might be Boston B&Bs such as the John Jeffries Inn in Beacon Hill or the Kendall Hotel in Cambridge.

I agree that you should check Priceline and also Travelzoo. As it gets closer you may find some good hotel deals. P.S. Avoid Best Western Roundhouse Suites and the Hampton Suites in Boston. Dicey area.