If you're low maintenance, check out one of these hostels...you can get private rooms, if there's availability. Hostelling Int'l has high standards. I just stayed in the Fenway one...it's a former college dormitory close to the Kenmore train station. Saved us a wad of money!
http://www.hihostels.com/dba/Hostels-Boston-list.php?lang=E&city=US%7C0010 about 8 years agoAnswered by Janet E. Dore via Travellr.com
If you don't want to go the hostel route you can always look into the courtyard Marriotts scattered around. One being right next to Copley sq and others being a bit further out of the city. They tend to be the smaller in the marriott chain, but clean and not ridiculously expensive like some of the bigger hotels in the middle of the city.
There's also a nice bed and breakfast not so far from Fenway on a back street, but I cannot for the life of me remember the name. almost 8 years ago