Is there parking or a parking fee?

Yes

For the Bay Spirit; The closest parking is right on Ocean St and at either end of the harbor. This is town parking. You pay at the pay stations or with the parking attendants. It's $2 - 3$ per hour (9/22/21) You can park for free for 2 hours at Old Colony Rd which is a 2 minute walk to boat and parallel to Ocean St away from the Harbor. *If your going out on Bay Breeze, 180 Ocean St (harbor parking mentioned above) is an 8 minute walk to get to Bay Breeze (147 Lewis Bay Rd)

The parking lot right by the dock does charge a fee, I think it was like $5.