Sounds like you will have one full day to explore. I would second Gardyloo's suggestion of renting a car and heading south of Anchorage to Girdwood/Turnagain Arm. Lots of things to do/explore. Girdwood has the tram. You can also hike he Winner Creek Trail to the hand tram, which is quite unique. If you don't want to do too much walking (it is relatively flat, but probably 1-2 miles each way), you can drive to the western trailhead on Crow Creek Mine Road and then it is only about 1/2-3/4 mile to the hand tram. You pull yourself across the gorge in the tram or others on either side pull you.

There is some gold panning available in this area too. The pay dirt is seeded but it is fun and gives you an idea of how things are done. Indian Creek Mine is less expensive and a bit less touristy than Crow Creek Mine.

The Wildlife Conservation Center is a bit further down the road where you can see quite a bit of wildlife (in captivity since they are injured or orphaned).

You can continue a bit further down Turnagain Arm to the Portage Glacier area. A nice flat walk to Byron Glacier allows you to see a glacier up close. If you are interested in seeing even more glaciers you can take an afternoon glacier cruise from Whittier. That would take up your afternoon. You need to go through the 2 mile long one-lane tunnel that is shared with trains and is only open 15 minute in each direction. 26 Glaciers or Major Marine are the two vendors for this.

Lots of options to do things in this area - way more than the time allotted!