Acadia National Park is covered with old carriage trails, definately worth doing. You can also ride from Bar Harbor over to Southwest Harbor and back through Seal Cove to Somes. Best to do road rides early before the tourists clog the roads. There are several ferries that take you to the surrounding islands, but most don't have more than 5 miles of road to ride on
Ascending or Descending the NH Mountains NW of Concord!
Snazzy* Schwinns, Classy Cannondales, & a Lonely '83 Santana Tandem (* Ed.)
The Carriage roads are great. I'll miss riding them for the first summer in three years. None are paved so riding with thin road specific tires would be a tough go. MTBs with slick or little tread 26 inch tires or hybrids with wider 700c are better suited. Also, take a pack or if you have a rack and bag for snacks and extra water. There are only a few places in the park to stop for refreshments, and I think I've only seen one that was close to the Carriage roads. If you are staying right in Bar Harbor, you can ride your bike to one of the Carriage road entrances (about a mile away). Maps are available and very helpful. Take your camara. There are many spectacular sights.