If visiting mactaquack and wanting to swim at the beach park across the street and walk over to the beach... otherwise you need to go into the provincial park, pay and park and then walk to the beach.
Personally, I find the York-Sudbury Museum to be a waste of time. If you want to look at old stuff from the 1800s or so, you're better off going to King's Landing.
However, the museum isn't entirely without merit. It is the home of the Coleman Frog, Fredericton's kitschiest treasure. This is theoretically the world's largest taxidermed frog, but it has been painted so many times over the years, it doesn't bear as much resemblance to a frog as Kermit would. Heck, Miss Piggy looks more like a real frog than the Coleman Frog!