The best time to go to any destination is after tourist season - for Maine, the month of september is great. Otherwise, all the tourists are there, making the places hot, crowded, and hard to get to.
I grew up in DC (the mother of all tourist destinations) and we didn't go down to the mall (tourist area) during tourist season (april through august) except to make fun of the tourists.
Also, the locals know where to go to access the beach and find parking. Your best bet is to browse around the web and check places like the tripadvisor forums for local information.