There is little to say about Katahdin. It is far from easy to get to the top (about a 5 mile hike each way with an elevation change in excess of 4,000 feet), but the views are stunning. It's the northern terminus of the Appalachian Trail for a reason. The through-hikers at the top alone can be worth the trek with their exuberant joy after finishing the 2,200 mile journey starting in northern Georgia. If you don't have time to make the hike, Baxter State Park is an excellent trip none-the-less, with a variety of smaller mountains and shorter trails to explore. Campsites in the park go quickly though so make sure you get reservations well in advance.
Not for the faint of heart Mount Kahahdin is the Terminus of the Appalachian trial. There is a set number of people that are allowed on the trail so get to park entrance early! The most amazing part of the of the hike was walking along the ridge line to the summit because every direction but forward was a couple thousand foot drop so it forced you to keep hiking forward
The Appalachian Trail starts/stops in Maine's Baxter State Park. Info and access isn't advertised as openly as you'd find at, say, Disneyworld -- many locals prefer it that way -- but the area is surrounded by hikes, ponds and streams to canoe or raft, and spots like this one.