Is there a parking structure for the museum, if so, how much is parking?

Usually you can find free street parking close by. The parking lot tends to be full on Saturdays.

There is a parking lot I parked there for 2 hours And it cost me $10

From their website: PARKING On-site parking is available in the lot behind the Museum, off Washington Avenue. On Target First Saturdays there's a flat rate of $6 beginning at 5 p.m.