Hi Pisces, welcome to the forum.
We've been to Boston a couple of times and trust me the hotels are expensive. Needless to say we've always stayed outside the city, the last time in Saugus, at the Days Inn, about 15 miles outside of Boston. BTW the hotel has a free shuttle to Logan.
As far as bicycling, it seemed to me that half the city commutes on bikes. One afternoon we went for a walk down by the Charles River and there was a very active bike/walking/jogging/skating path. I think the path goes pass the Museum of Science, but as I had an ice cream emergency ( my two scoops fell off the cone ) I didn't get that far.
For more Boston info drop a line to Donna, the Phoenix correspondent, she helped me when I was planning my trip.
Have fun and watch yourself in the rotaries.

Keep'em flying