Bass Harbor Lighthouse on Mt. Desert Island is worth visiting . . . I did the catamaran whale watch out of Bar Harbor and felt it was decent . . . don't just do the park loop in Acadia -- hit the highlights (and be sure to time Thunder Hole at the right time of day . . . otherwise you will be disappointed and wonder what the big deal is), but be sure to do some hiking and get off the beaten paths where some tourists rarely tread.
The candy shop/ice cream shop in town is a nice way to finish the day . . . although I'm still not quite sure about their lobster ice cream concoction.
I'm not sure if it's still there, but there used to be an old time clock maker/repair shop in town (there was another which had a lot of cheap novelty clocks for sale) . . . you would descend some steps and instantly be transported to a different time as the owner was almost always smoking a pipe and the ticking and tocking of the cuckoo clocks and other clocks surrounded you . . . I always liked going there.
Sand Bar Island . . . fun hike . . . not sure if you can still drive your personal vehicle over at low tide . . . but regardless of whether you drive or hike across . . . be sure to not get caught on the island with the high tide coming in.
Hey that's my neck of the woods, I live in Bass Harbor, on the "Quiet Side" or the "Back Side" of Mount Desert Island. That "Desert" is pronounced as in the after dinner sweet, so named because Samuel deChamplain described the Island as "mountainous and deserted (void of inhabitants)" when he "discovered" the Island. Also, just so you know it is A-cadia, there is no "R" in there.
Here is my short must do:
1. The Park Loop Road, pretty obvious. Don't be afraid to stop at some unassuming, un-namded turn out and explore a little. Thunder Hole is best on a rising tide a few hours before high tide, with a little wind, and some bigger waves you might get lucky and see a show. Tides are about 6.5 hours between low and high.
2. Sunrise and or Sunset, on top of Cadillac Mountain, the first place to see sunlight in the U.S. There is a road to the summit if you are not the hiking type. If you are the hiking type, pick a mountain any mountain, you can't go wrong, two of the best would be Champlain or Dorr.
3. Eat a fresh cooked lobster. Do yourself a favor and do not order a lobster dinner from a traditional "restaurant", it is likely pre-cooked and re-heated when you order it and probably half dead when they did cook it. Go to a "Lobster Pound", so named because they do lobster and that's about it, you pick out your lobster and pay by the pound, get some steamer clams to go with it, bring your own favorite beer and your good to go. The lobster was probably caught that morning, and if the pound knows what they are doing they boil the lobster in sea water. My favorites are "Thurstons" in Bass Harbor and "Trenton Bridge" in Trenton.
Bar Harbor is lined with shopping if that is your thing. The ice cream shop Jake mentioned is right in the middle of Bar Harbor, "Ben and Bills", no relation to Ben an Jerry. You can drive your car over the bar to "Bar Island", just be sure an check the tides, there is a picture in the paper every year of a tourists car being swallowed by the incoming tide.
Not to burst your bubble about the whale watching, but if you are lucky you might see a bit more than a hump, a tail or a blow. Breeching is rare. Any of the outfits that go out of the pier in Bar Harbor do a good job. If you've got kids or are a diver, "Diver-Ed" is a great trip.
Hunters beach in Seal Harbor is a magical place, if there are more than 3-4 cars in the parking area, consider coming back another time. Seawall, Wonderland, Ships Harbor, and the lighthouse at Bass Harbor Head are nice stops on my side of the Island.