+1 for Denali. Pretty amazing place, especially when the mountain is "out."
An overlooked, but spectacular, park is Wrangel-St. Elias in Alaska. It's the largest NP in the USA. I spent a few summers living on the park's doorstep in Glennallen, Alaska, waking up every morning looking at the Wrangell mountain range. Beautiful. A cool drive is along the McCarthy Road - an old railroad bed from Chitna to McCarthy, right into the heart of the park. You'll cross a deep gorge on a century-old railroad trestle and end up at a glacial river. Cross the river on the pedestrian-only bridge (used to have to pull yourself across on a two-person cable tram) and then hike up five miles to the mining ghost town of Kennecott. See http://www.nps.gov/wrst/historyculture/kennecott.htm
The road into McCarthy/Kennecott is dirt, but passable by most vehicles. A much rougher and more interesting 4x4 road goes south from Chitna toward (but not to) Cordova, again along the abandoned RR bed. At one point the state of Alaska was thinking of turning it into an overland route to Cordova, but gave up because of the cost. I'm not sure of the current state of this part of the "road," as it was years ago that I drove it. But it was really cool, with old cabins, tunnels, etc.