Do this the first day because you won't have time on the second.
1. Get a car
2. Drive to Whittier via the
Seward Highway (around 90 min.) on one of the most scenic highways in North America. Stop for breakfast en route at the
Bake Shop at the Alyeska ski resort in Girdwood. Recommend the cinnamon rolls.
3. Go through the
Whittier tunnel and take a
"26 Glacier" cruise.
4. Return to Anchorage and stay at the Hilton downtown. Dinner at the
Glacier Brewhouse or
Simon and Seafort's where in June you can watch the sun try to set (not until almost midnight) over Cook Inlet.
5. The next morning, before the airport visit the
Alaska Native Heritage Center to get a sense of the many cultures present in Alaska. It's much more than moose and mountains.
http://goo.gl/maps/x6YC1