We've stayed at the Parker House many times, and the proximity to Fanueil Hall and the North End is tough to beat. My favorite North End spot is Carmelina's, but you'll definitely need a reservation, Mamma Mia's and Giacomo's are good options. Neptune Oyster is up there too. It's really good and walk-in only. Don't skip the Mike's Pastry experience (cash only).
On our most recent trip we stayed at The Newbury, and it was awesome. Saltie Girl is a few blocks away if you're looking for seafood. The hotel's fine dining restaurant is Contessa, which I understand is notoriously fussy so we skipped, but we had a great breakfast at The Street Bar on the first floor. Good spot for a short trip and a block away from the Arlington T stop.
Get last minute tickets to a Sox game, go walk around the bars on Landsdowne before hand, and stay for as much of the game as you want. There's no place like Fenway, and if the investment isn't huge, you won't feel guilty sneaking out early once your daughter has her fill.