Maine has a beautiful coastline, and people have been going there to be awed by it's beauty and diversity for a long, long time! Acadia National Park is located right in the midst of allll that splendor!! This park is the place to go, and also contains the tallest mountain on the Atlantic coast!
Tourists come here to see the sights, hike granite peaks, visit historic roads, and more! If you go during tourist season, you'll see the sights, but it will be crazy crowded and you might not find parking. But, you'll love your time there no matter when you go!
I visited in November and while it was cold and a bit snowy (especially on the ridge-lines) it was great to be able to experience the island without the distraction of other people! The towns were all quiet, many of the shops and restaurants were closed, and the locals were the only people still left in town until the weekend. And, the hotels that were still open in November offered great prices.
One place you should visit if you're a thrill seeker is Precipice Trail! It's easily one of the most popular and dangerous trails in the park. I wouldn't recommend it while raining or shortly after rain because it can get very slippery and very dangerous. But you follow all warnings, and make sure you have a good stand, you'll be just fine! The view and the feeling after completing it are simply stunning. There are, I should mention, much easier ways to get to the top and get similar views, but none will provide the same rush!
I really can't choose the best one for you!!! Check out all the trails and trail reviews on everytrail. You'll probably have a hard time choosing, too: http://www.everytrail.com/best/hiking-acadia-national-park