Acadia walks along the old carriage roads to more strenuous hikes. This website has a list of really great hikes (copy/paste into your browser): https://www.citrusmilo.com/acadiaguide/recommend.cfm Hiking up Penobscot on the cliff side, then cutting over to Sargent Pond (Maine's first pond!) for a quick dip is really fun, but be in good shape, because it is a bit strenuous: https://www.citrusmilo.com/acadiaguide/penobscotmountain.cfm
The best popovers you'll ever have. Really good lemonade as well. Be sure to make a reservation, as it can get busy. If you sit outside, be careful of the bees. Insider tip: book a table for the early afternoon, then get there early enough to enjoy a 3.4 mile walk around Jordan Pond, so you can enjoy tea and popovers after your walk.
Unfortunately, this is only accessible by renting a boat. If you can get there, I recommend anchoring and rowing in, then dragging your boat safely up the beach past the high-tide mark. Pack a lunch, look at the graveyard, and walk along the paths. There is a lighthouse at the topmost point of the island, that it is no longer in use. On the eastern side there is Table Rock, which is where I recommend eating your sandwich.
This is an island that is accessible by ferry. Very beautiful with a lot of trails. If you walk up the main path from the dock, there is a general store where they sell all kinds of things. If you keep walking along the road, just past the tennis court, you will come upon Hitty's Cafe where they sell delicious sandwiches (really great lobster sandwiches) and pastries.
Discover the history of the Cranberry Isles. This small museum is open from 9am to 3pm in September. The museum is located right off the museum dock. Since you'll be right near the dock, there is a really great gift shop on the dock, next to a fantastic clay studio. Both stores are worth checking out. Next door to the restaurant is an art gallery featuring local artists.
Bar Harbor offers shops and restaurants, and a very Maine vibe. If you like museums, check out the Abbe Museum to learn about the indigenous peoples of Maine. If you like gardens, the Asticou Azalea Garden, part Japanese garden and part azalea garden. Or Thuya Garden that has a 1/2 mile walk to an observation point. Both gardens are free. If you want to rent a boat or just tour around on a lobster boat, looking for that service out of Bar Harbor is probably your best bet.
Somes Sound is a beautiful fjard (according to Wikipedia: "While often described as the "only fjord on the East Coast", it lacks the extreme vertical relief and anoxic sediments associated with Norwegian fjords, and is now called a fjard by officials — a smaller drowned glacial embayment."). The best way to enjoy the views by car is to drive along Sargeant Drive. If you can rent a boat, I recommend packing a lunch, throwing down an anchor, and enjoying a swim.