Since it is hard to get everyone to agree on what to do, you may want to split into two groups and spend the day doing different things. I would suggest renting a car for the day and drive around the area. If you are interested in the Iditarod dog sled race, there is a very interesting museum in Wasilla. Wasilla is only about a 45 minute drive north from Anchorage.
I can't say how many people I have seen that just sit at the Anchorage airport from before noon and waiting for a flight that leaves at nine or ten at night. What ever you decide to do, enjoy your time in the Anchorage area.
Debra