There is absolutely nothing of interest around the port. I don't know about public transportation there right now since a massive public construction work is going on. Here is a link showing you how far away from everything the Black Falcon pier, which is used by cruise ships, actually is. Take a cab to wherever you want to go.
Carol, when I went into Boston and Black Falcon, the trolley and buses made stops at the pier. The Trolley would be a good fast way to see a lot of the city without getting lost or exhausted. I happen to recommend this to alot of visitors to my company and I just confirmed with Old Town Trolley (617 269 7010), that they have a shuttle bus that brings cruisers from Black Falcon Pier to their departure point near the Aquarium. This 100 minute tour (if you stay on the whole route as you have the option to get on or off) costs $23 per adult. The guide will give you a complete history and overview of the city. Boston holds many historically wonders and should not be missed. Will you be in port when the Summit is here for TA inspection the week of Sept.16?
That is a VAST improvement over how it was the last time I was there. Black Falcon Pier is a very nice cruise terminal and Boston is a fantastic port, but it was so desolate when we were ther. Fortunately we'd had a week in Boston pre-cruise. I went to school up there and really love it.
The short answer is that there is nothing of interest within walking distance of Boston's Black Falcon Cruise Ship Terminal -- not even a transit stop. MV Royal Princess had a shuttle to downtown Boston. My experience in Europe this past summer is that Princess's shuttle bus service seems to cost $4.00 each way, regardless of distance, and to operate every half hour between the pier and a designated point in the center of town.
Once you get to downtown Boston, all the major attractions are within walking distance and there's an excellent transit system. For those who have not been to Boston before, the Freedom Trail -- a route marked with a double stripe of bricks in the sidewalk that goes by about fifteen historical attractoins -- is an excellent stroll for a nice day. For those who have difficulty walking, Beantown Trolley Tours runs tourist buses that look like old trolley cars along essentially the same route. With an all day pass, you can get on and off the trolley buses as you wish.
For a more interesting and scenic tour of Boston, head to the Prudential Cener and take a Duck Tour aboard an amphibious vehicle that transits the Charles River in addition to the city's streets.
Boston has several worthwhile attractions for rainy days, too. Boston's Museum of Science, Museum of Fine Arts, Isabella Stewart Gardner Museum (which, BTW, has quite a story behind it), Computer Museum, and New England Aquarium are a few of the options in the downtown and "Back Bay" area.