Several opportunities that I have taken.
Rented a 172 at Palmer, with an instructor in right seat, flew up over the glacier there.
Flew on the mail plane from Fairbanks, to Central, Circle, Eagle, and back to Fairbanks. With no reservation, the round trip was about the cost of a single leg for regular passage. Purely space available, though, filling seats in a less than full flight.
Mail planes fly out of several airports, similar deals may be available at all of them.
Float planes fly fishing parties in the morning, and back out in the evening. In between, they can give you sight seeing flights. They fly from most towns and cities.
Don't try to book a flight out of the old main airport in Anchorage, it is a madhouse, and the wait for a clearance to depart can take up to an hour. It must be the busiest GA airport in the world. Took a local friend, he filed his flight plan, they told him to call on the radio in half an hour for a taxi clearance. When he called on his handheld, he was about tenth in line to enter the taxiway to the runup area, and 20th for departure. He had flown a patient in to the hospital, and was returning to his cabin in the woods.
Don't bother to try to fly when the visibility is poor, or there are low clouds, it is a waste of money and the great views are missing. It is beautiful up there.
