I found that though there are places to rent on the trail, they're pretty hard to get to unless you already have a car (or a bike). What was simplest (though a bit more expensive) for me was taking the metro to the trail and renting one of the bikes from the automated machines:
I biked all the way to Walden pond and back.
Great suggestion, Brandon, and useful to future posters looking for biking advice. Hubway is the regional bike sharing program in the Boston area. www.thehubway.com It's too bad that there are not currently Hubway bikes at the Alewife Red Line station, which is both at the end of the Red Line subway and the intersection of several bike trails, including the Minuteman Trail. So the Davis Square Red Line stop is the closest place to the Minuteman trail to rent a bike that is also transit accessible.
In addition to the bike store mentioned above in Arlington, there is a bike sa/es/rental store at the Bedford, Mass end of the Minuteman trail, but it is not as easily accessed via public transit as the Hubway. http://www.bikewaysource.com
[ I am not affiliated with any of the businesses mentioned above].
Quad Cycles in Arlington rents bike. It's right on Mass Ave so next to the bike path and right on a bus route so easy to get to. BikeStop, mentioned by the first response, would also be easy to get to and it's literally right on the bike path.
Another rental option is the Bicycle Exchange (2067 Massachusetts Ave. in Cambridge). It's about a 5-minute walk from the Porter Square station on the MBTA red line. Then from the bike shop to the start of the Minuteman trail is about a 5-minute bike ride via city streets that are relatively tame, except for the short initial stretch on Mass. Ave. itself. (And just to be clear: I have no business interest or affiliation with this shop.)
This worked well for me today, because some of the others are closed on Mondays and Tuesdays.
The minuteman trail runs into the battle trail , if you stop @ the Lexington visitor centre which has a back door on the trail, pick up a map and directions to the minuteman national historic park.
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