When DF came in November, we rented a flat off of airbnb.com, but we stayed in Quincy for 10 days because it was cheaper and a 5 minute walk from the redline, but the site had a lot of options.
As far as getting out of the city, I would recommend what everyone already said, but would also toss Plymouth into the mix. If the weather is nice, you could also head to some of the beaches (Marshfield, Duxbury, Nantasket).