Is there parking at the Neptune Oyster restaurant in Boston? If yes, how much does it cost? If no, where would be a close place to park for the best price?

No, they don't have parking. Best to use Uber or metro in that area.

They don’t have parking

We parked in the garage that is part of the Boston Public Market. It is a short walk (about 2 blocks) and if you buy anything at the Boston Public market before or after your meal at Neptune Oyster the BPM merchant will validate your parking for $1/hour up to 3 hours.

Nope

No parking. The is on the street parking, but they were full when I was there.