Peter:
Everyone has different priorities, but for me, Anchorage was the most expensive and the least interesting place that I visited in Alaska. The setting is spectacular, surrounded as it is by snowy mountains, and right on the water (the Cook inlet). There is history in the city, and a museum or two, but honestly, (and this is strictly my opinion), a single full day should cover the highlights, and you're not likely to miss anything important if you leave it at that. There's so much to see in the rest of Alaska, your time would be better spent on the road.
Rick