My advice would be to be flexible about when you come up to Boston. Hotel reates really fluctuate. For example, on Patriots Day weekend rates are very high and it is difficult to get a room. Sometimes there are big conferences in town and rates are high. Personally, I use priceline's name your own price feature. I select the Copely square area and 3 1/2 stars. I have gotten rooms as cheap as $85 (Fairmont), $110 (Copley Mariott and Westin). If you want to go down to 3 stars or under, you can get a better deal. Once you have the hotel locked in, then worry about game tickets. Since you are coming from Florida, sign up for some price alerts to Boston. JetBlue has this as an online feature, so does the travel site kayak.
I'd track airline rates and hotel rates first and book them at the same time. You have to track them both, because sometimes airline rates are high when the hotel rates are low and vice versa.