No surprise: Some places allow pets, some don't. We've noted inns that allow pets, but even here I don't recommend showing up with a pet in tow unless you've cleared it over the phone with the innkeeper. Note that many establishments have only one or two rooms (often a cottage or room with exterior entrance) set aside for guests traveling with pets, and they won't be happy to meet Fido if the pet rooms are already occupied. Also, it's increasingly common for a surcharge of $10 or $20 to be charged to pet owners to pay for the extra cleaning. On the positive side, all Motel 6 hotels accept pets as a matter of policy, and so (surprisingly) do some upscale inns.
Keep in mind that dogs are prohibited on hiking trails and must be leashed at all times on federal lands administered by the National Park Service (this includes Acadia National Park in Maine). Pets are allowed to hike off-leash in the White Mountains National Forest in New Hampshire and the Green Mountain National Forest in Vermont. No pets of any sort are allowed at any time (leashed or unleashed) at Baxter State Park in Maine. Other Maine state parks do allow pets on a leash.