If it were me I would stay at the Omni Parker House
https://www.omnihotels.com/ You can get an executive room there which has 2 double beds and a pull out couch in the $250 range.
It is right across from the Park Street T which will connect you to just about anywhere you want to go. It is a great place to stay and you can walk anywhere it is centrally located across from the Boston Common/Flower Garden , next to Fanueil Hall, Downtown Shopping District/Macy's etc., Newbury Street which has lots of restaurants and shops, Prudential Center/Mall , Eat lunch in Chinatown, I'll send you our favorite restaurant there for an inexpensive authentic meal , Charles Street resturants and shops, museum of science, north end restaurants and bakeries, aquarium. You can take the T over to Cambridge in about 10 minutes and walk around Harvard square. Check out the chocolate buffet at the Langham hotel on Saturdays,...yummy we just went over the holidays so much fun.
http://boston.langhamhotels.com/restaurants/chocolate_bar.htm
Can you tell I love Boston? I grew up in South Boston and have gone back at east once a week, sometimes multiple trips each week to meet with friends and family. I don't think you need to rent a car to go anywhere, there is so much to do there. I could go on and on....Enjoy Boston!!!!!!!!