I would grab that $225 a night. It's a great rate for Boston, especially for that weekend. That way you drive in leave you car at the hotel and be done with any extra transportation. Gives you more time in Boston.
However, if that is still out of your budget, as pp's have said look at Braintree/Quincy (South), Needham/Newton (West), Woburn/Burlington (North), and East Boston/Revere. Although the T will be busier then normal that weekend I would not try driving in and out everyday as that will be even worse.
Another cost factor will be if you stay out side the city and take the T. The subway portion of the T, it will cost between $2 (with a Charlie Card) and $2.5 (with a paper Charlie Ticket) a trip the Commuter Rail portion of the T from some of the areas mentioned will cost about $6.00 each way, prices go up the further you go from Boston up to about $10 each way. There is no free transfer for single ride tickets from the commuter rail to the subway. So you could be looking around $16pp and up to take the T in from the burbs. Taking that in and out a few days and it starts to add up, especially when you have to pay for parking at the T lots. The Revere/East Boston locations would be the regular T subway fares, for between $4 and $5pp round trip. Some places do have free shuttles to the T so you could save parking costs that way.