Someone said to skip Maine unless you were going to Bar Harbor. Please ignore that advice!
Bar Harbor is a decent little tourist trap, but it is not the reason to go to that area of Maine. Bar Harbor does have its good points: there are historic homes, cute little shops (but mostly trinket stuff unless you're looking to spend good $$), some nice restaurants, whale watching cruises, and beautiful views. It's also ridiculously overcrowded June --> Labor Day, but worth it if you really want to see it. The reason to go to Mt. Desert Island (which is the island Bar Harbor is on) is for Acadia National Park. Absolutely beautiful! Great hikes, scenic views, wildlife, etc. You won't be disappointed.
Now, another poster mentioned that there's a lot of driving in Maine, and that's true. But, you can chop it up into smaller portions if you're strategic and get to see a decent portion of Maine while you're at it.
Here's what I'd recommend (this is assuming the idea is to see as much of Maine as you can and that you don't have the money or the will to just hang out at a ridiculously priced inn in Ogunquit or Wells):
Portland & Freeport
Portland is only an hour from the NH/ME line and is Maine's largest city (~65k people
). There are plenty of things for a family to do-- museums, Funtown/Splashtown amusement parks (small for what you might be used to, but your daughter will probably love it), scenic and seal cruises, thriving art scene, tons of restaurants/pubs/taverns and the city's becoming known for its "foodie" cred, Portland Sea Dogs games (Double AA team for the Red Sox), paddleboarding/kayaking, the iconic Portland Head Light, etc.
Freeport is just 15 minutes North of Portland and is home to the Desert of Maine (which is just fun because it's such a strange thing and it's kind of an inside joke in Maine and not many tourists seem to find their way there) and to dozens of outlets. This is where the L.L.Bean flagship store is and they often have exhibitions in the store during the summer and early fall, like fly fishing tutorials, etc. Have your picture taken at the big boot! If your family likes to shop, Freeport is probably one of the better places in Maine.
If Freeport doesn't sound like your thing, 30 minutes South of Portland is Old Orchard Beach. This is kind of like Atlantic City's
little little sister-- sand beach, amusement park, shops, etc. But, if you're going much past mid-September, you might find a lot is closed.
Rockland/Camden Area
Rockland and Camden are about an hour and 20 minutes North East of Freeport (you'll notice that in Maine, we give distances in time! lol
). They're both just pretty little towns with a nice slow pace and gorgeous scenery. There's: the Rockland Breakwater Light (wear sturdy shoes), shopping and good restaurants downtown, Owl's Head Light, The Strand Theatre, Mount Battie, etc. There's more than enough to explore for a day or so.
Bar Harbor/Acadia National Park
Bar Harbor is about 2 hours North East of Rockland. I already mentioned what BH and ANP have to offer. ANP makes it definitely worth it!
So...if you make it to Bar Harbor, you're about 4 hours into Maine. Castine would be a nice place to visit on the way home, but you might find it to be a little more of the same unless you happen to hit it at a time when the sailors from Maine Maritime Academy is shipping out and I really don't remember when they do that. Hallowell is roughly half-way between BH and New Hampshire and pretty close to I95 so it's convenient. The Liberal Cup is a local favorite and there is a cute little downtown.
This list is far from all that Maine has to offer, but it is some of the best, and I tried to suggest places not too far from the interstate and that were convenient to one another so your time experiencing Maine was maximized, rather than spending most of the time in the car!
Please don't skip Maine! It's a great place to vacation