If you want to park for free and don't mind walking, there are places 1/2 mile away in town
If you park at Doubleday Field, it's free. As far as the museum, just show your card, get your hand stamped and you're good to go.
Some parking has a small fee, but you should be good to go if you have the membership.
Currently, parking costs $0.50 per 15 minute stay with a max of 2 hours allowed. Every two hours you stay at the museum would cost you $4.00. If you use the trolley, it is $2.00 per person/pass and you could use that pass to get around Cooperstown all day. The parking at the trolley station/area is free.
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