Schoodic Point is the far eastern part of Acadia and is frequently the quietest part of the entire park, due to it's secluded locale. The waves roll into the rocks all hours of the day, but the best times to go are just before a storm or at a very high tide. The rocks are incredibly slippery and usually there are warning signs (and common sense) that warn caution on the rocks; the waves have been known to pull people into the water and few have survived such an ordeal.
Cadillac Mountain is the tallest mountain in the park and many drive up the mountain to see the sunrise, as it is the first spot in the United States to see the sun. On a clear day the views are spectacular and I've even seen Katahdin in the distance. There are many hiking trails on the mountain and ambitious bikers frequently bike up (and down) the two lane road that winds to the top.
See a lighthouse, or several.
Take a boat out and explore some of the islands. We took a little cruise boat out and had the opportunity to boat around the various islands and had a short stop on Little Cranberry Island. A boat tour is a great way to see the terrain from the water and experience more of the nature then simply driving around or even hiking!
Visit Sea Wall. There is also camping nearby. The water rolls the stones around until they're perfectly smooth and round. The sounds of the waves and the rocks is unique and has to be experienced.
If you're had enough of the outdoors, there is always shopping Bar Harbor. It's touristy, but great to pick up souvenirs! There are plenty of maps at most of the stores, and before you get onto Mount Dessert, there is a visitor's station with information about the park and what to see.