Anywhere on the coast is beautiful even this time of year. I like Boothbay, Camden, Rockport, Belfast. Or you could come all the way up the Maine coast and have Caue and Oakly show you their stomping grounds.
Kara, if you want to stay a night at The Inn By The Sea in Cape Elizabeth, you'll love it. http://www.innbythesea.com/They have welcome bags for dogs, and even a doggie room service menu. There's a boardwalk down to crescent beach, but I'm not sure it's passable in winter(?). Ferry Beach in Scarborough is dog paradise, a real maine beach with working lobsterman and dogs officially welcome off leash. Dinner in the Portland's Old Port is fun, and LL Bean/Gritty McDuff's in Freeport is entertaining. The Haraseeket Inn in Freeport is pretty, welcomes dogs, and serves a heck of a Sunday brunch. http://www.harraseeketinn.com/ I'm in Falmouth, and we're available for golden babysitting, kissfaceying,and playing if you need a babysitter to go out to dinner, shop, sight see etc.