There is no cheep parking
I took the train too since its right across the street from td garden but i walked around the surrounding areas and i saw free street side parking about a 3 minute walk from td, near the sheriff's station.
I personally don't know I usually just stay at a hotel, and uber around.
Sorry took the train there. Cheaper, no traffic.
You can find a cheap parking near TD Garden at Avalon North Station for only $10 (2hours). But reservation prices may vary Don't really know if you can get it for many days
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