Well, that's funny, I am heading there tomorrow as well, will be back on Sunday... I am will be doing the tourist thing as well (I have been there before, but the woman hasn't), we may run into each other...
The airport is very close to downtown, however there is $6 in fees/tolls leaving the airport. According to the Logan Airport most downtown hotels are about $15. Don't know if that includes the fees, it isn't clear.