Juneau

Juneau needs 2 days: the Mendenhall Ice Field and its namesake glacier, visible from a viewpoint 20 minutes from downtown, on one, and a boat excursion through Tracy Arm Fjords National Monument to see humpback whales and glaciers calving into the water, on the other. May-September is best and the only period with regular cruise access. It's expensive, with all logistics dependent on boat or plane. It's the only US state capital with no road connection to the rest of the country -reachable only by ferry or plane-, and its bay is one of the most visited stops on Alaska cruises, with glaciers, whales and bears accessible on day trips.