If you want to lie on the beach, do not go to Maine. But if you like a rocky coast (and cold water), old inns and white clapboard houses, and the best lobster you've ever tasted, get thee to Maine.
Virginia may be for lovers, but Maine is for hikers, bikers, boaters, kayakers, explorers, antiquers, photographers, history buffs, lighthouse aficionados, and eaters.
First of all, if you want to go to Maine, stick to July and August, the warmest months. It'll already be a little cool in September. As they say in Maine, "We have four seasons in Maine, early winter, mid-winter, late winter, and next winter." The exception is July and August, when it'll be as my wife would say warm, but not too hot.
Second, the best way to experience Maine is to stay in an old inn or rent a house. There's plenty of listings online. There are also a lot of very good bed and breakfasts. There aren't many chain hotels or resorts.
Maine is actually a pretty large state, so there's a lot of places to go. A perennial favorite is Bar Harbor. There's good reason for its popularity, of course.
It might be a little touristy, but it's a lot of fun. It has all the amenities that will make your stay enjoyable from puffin and whale-watching cruises to places to rent bikes to cute shops to plenty of restaurants with good "lobstah" and "chowdah." And speaking of the food, you'll want to be prepared for a few New England classics, such as grape nuts pudding and whoopee pie (two cakey cookies sandwiching thick cream). They're weird, but kinda good.
You want to try those things for fun, but you'll want to be sure you prioritize getting your fill of lobster rolls and fresh blueberry pie, crisp, cobbler, etc, etc.
Once you're done eating, you'll find Bar Harbor is a good place to work it off. It's right next to Acadia National Park, and while I'm not really one for scenery, it is truly beautiful. Like most places at such high latitudes, the coast line has a distinctive look, as though the continent is frozen in the process of forming, or disintegrating. Nowhere is the effect more dramatic than in Acadia.
If you're looking for a louder vacation, I can also recommend Portland.
Portland is a small city that slopes down to a bay. The waterfront district feels almost like a small city in England or Ireland. It boasts a range of restaurants I've had some excellent sushi and bars, a wider variety of shops, and even a farmers' market. It's a fun town, with pretty good nightlife.
The bay itself offers good sailing and several historical oddities, including a Civil War-era fort, which just proves that the pork-barrel buffet is nothing new to Congress.
In the bay is Peek's Island, where we last rented a cottage.
The island, just a couple miles long, has a couple bars, a very charming inn, a coffee shop, and a soda fountain. It even has a grocery store whose motto is, "if we don't have it, you don't need it."
The island is a nice way to vacation in the country, in such a way that you can easily visit the city (there's a regular ferry service, which is not cheap). Were we to go back to Peek's, I would definitely consider the very beautiful inn.
You can also easily visit Portland if you're in Bar Harbor. It's two-and-a-half hours up the coast, so it would make a nice over-night side trip.
If you do get near Portland, be sure to visit the Two Lights Lobster Shack in Cape Elizabeth (20 minutes south of the town). It has regularly been voted the purveyor of the best lobster roll in Maine. I never go to the Pine Tree State, without a pilgrimage to this gustative Mecca.