where to sleep, where to eat and where to catch a red sox game
The Antica Torre di via Tornabuoni is a great place to stay if you like more apartment style living and value a roof deck bar with the panoramic views across the roof tops of Florence.
I can personally recommend room 503 as it has a large private terrace.
If you're hungry for dinner, around the corner from the hotel is the Parione. I can recommend it based on great food and minimal to non-existant tourist infestation. They do speak english, but this is truly a local Italian resturant. The night we were there we were the only people speaking english over the table in the whole place (and if you like that, you'll like Parione).
And btw... if you care about silly american sports... they can be found at the "house of sizzle" (insert joke here) and the Lions Fountain Irish Pub. They both have mlb, nba and nfl and you can call ahead for schedules.