Are You at the Sheraton @ 39 Dalton St. ?
There is a 60 space Open Lot at at 53 Belvidere St. for $28.00 for 12 Hrs.
The garages seem t be too low , and the other open lots are Valet Lots .
How many days will You be here for ?
For just one or two night's , You could sleep in the Walmart parking lot in Framingham ( there are Trucks and RV's there every night ) , then either drive in , or park at a local train/subway station and take a train or subway in .
( Riverside is Manned , the other T stations unmanned and are Pay By Phone to park as of this week )
http://en.parkopedia.com/parking/garage/hynes_auditorium_garage/02115/boston/
Another choice , if here a couple of days would be to stay at Normandy Farms Camping Resort in Foxboro and with a short 25 mi ride to riverside station , park and take the subway in , or a 5 min. taxi ride to take a train from Mansfield .
Basic Tent sites around $ 41 up to $ 66 for elect and cable .
http://www.normandyfarms.com/
And You can take your shower in one of the air conditioned rest rooms before jumping into one of the pools or hot tubs .
Another Option for camping
https://minutemancampground.com/
They also suggest parking RV's at Riverside and taking the T , for Prudential Center area .
Bob