Big question – I have no idea what you like.
Despite its proximity, I haven’t spent much time in Maine. The good stuff has already been mentioned – see Mt. Desert Island, with Bar Harbor if you’re up that far (It’s a 6 hour drive from Boston!!!)
Portland’s got interesting shops. So does York Beach and that area. See Kennebunkport for the shops and Bush I’s residence. See the outlet stores at various places.
Lots of used book shops along US 1.
I’ve always wanted to see the Shaker community at Sabbathday Lake – it’s the opnly one with living, working Shakers. Since the mid-90s they’ve allowed new Shakers in, so they might not die out as we’d feared (the surviving Shakers before that were all aging women).
Jump into the ocean anywhere along the Maine coast. Then spend the rest of the day trying to warm back up.
I love New Hampshire. as noted above, see Franconia Notch, with the Flume, the remains of the Old Man or the Mountain, the Whirlpool, Cannon mountain with its aerial tramway. If you still want to see stone profiles there is or at least) used to be a mini-Old Man visible on the Mount Washington Cog Railway, and there’s a stone Indian Head visible at (where else?) Indian Head.
Go to Clarke’s Trading Post and watch the trained bears and the east European mini-circus and the fake old-time Americana (rescued from Freedomland) and the real Americana that’s been prerserved there. Ride the railroad and see the Wolfman perform.
Go to Polar Caves and hike through the glascial boulders. Try to squeeze through The Lemon Squeezer. Feed the deer and the ducks.
Go to America’s Stonehenge and see if you buy their theories abnout this place being an ancient sunrise/sunset observatory. Or if you buy it being an inspiration for H.P. Lovecraft.
Go to the Canterbury Shaker Village. No shakers, but it’s the best preserved, and you can get lunch.
Go to North Conway and Crawford Notch. Lots of obscure hiking trails with hidden waterfalls.
Drive the Kancamangus Highway and see the scenery. Do not take our daughter, who will be bored by it all.
Go to Castle in the Clouds and take the tour and ride the horses.
Go to Laconia or weir’s Beach or somewhere else on Lake Winnipesaukee.
Go to Squam Lake Nature Center and see the animals and the exhibits.
Go to Ruggles ine and dig up bits of mica. Or, if you’re lucky, gem stones.
come to Massachusetts and see Boston and Salem. see the many preserved villages – Sturbridge Village, Plymouth Plantation, Old Salem Village, Fruitlands Museum.