Closest is at the Seaport Hotel in the South Boston Waterfront neighborhood, approximately half a mile from the cruise port, where an office of Select Rental Cars is located. Google "select rental cars seaport" and see what you think about the opinions on Yelp.com, which should come up in the results.
Almost as close is South Station, where Hertz has an office.
You can easily get to both the Seaport Hotel and South Station on the Silver Line bus, which has a stop just outside of the cruise terminal - about a 5-10 minute ride. You can find information and a map with both of these locations and the cruise terminal on Boston Discovery Guide's South Boston Waterfront page.
Another good option is to take a water taxi from the cruise terminal to Boston Logan Airport - about 8-10 minutes - and pick up an rental car from the company of your choice there. Check Boston Rental Cars for more information about the different car agencies at the airport.
If you're going to be driving in or near Boston, be sure to check out my Boston Driving Tips, so that you get a sense of our narrow roads and crazy drivers before you encounter them close-up.
Keep in mind that unless you want to go outside of central Boston, you don't really need a rental car in the city. Unlike lots of cruise ports in other places that are some distance from the main part of town, Boston's Black Falcon Cruise Terminal is just a few blocks (a 5-10 minute walk) from one of Boston's trendiest neighborhoods, which is adjacent to downtown Boston (another 5-10 minute walk).
Good luck with the car (and, um, Boston drivers), and have a great time in Boston!
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