Well of course you should extend your time if you can.

Depending on how many additional days you can manage, there are umpteen things worth doing, both in Anchorage and farther afield.

For example, by late August autumn is definitely on the way in Denali National Park (around 5 hours by car from Anchorage.) The colors on the tundra, fresh snow on the higher mountains, no mosquitoes... terrific.

Or ride the gondola up to the Seven Glaciers restaurant on top of the mountain at the Alyeska resort in Girdwood (just up the road from the Whittier tunnel entrance.)

Or head down to Seward and go on a Kenai Fjords cruise - glaciers, whales... Or while you're there, go fishing for some of the late silver salmon that crowd Resurrection Bay.

In Anchorage, visit the Native Heritage center, or shop for wonderful native crafts at the Alaska Native Medical Center gift shop. Or head up the road to Eklutna, a native village with a fascinating graveyard full of painted "spirit houses." Stop at Mirror Lake, especially if it's an early fall and the leaves have started to turn.

Or hop on a floatplane at Rust's and go watch bears, or fly up to Denali (if you don't want to drive) for a never-forget experience (even for us jaded flyers, approaching Denali in a light plane will leave you gobsmacked.)

Or for a terrific off-the-path experience, use some Alaska or AA miles if you have any for an overnight visit to Kotzebue, an Inupiat Eskimo village on the Arctic Ocean above the arctic circle. In late August/early September things will really be hopping as folks finish up summer fish camps and start getting ready for winter. The main hotel in Kotz is very comfortable, doesn't cost a lot more (if at all) than Anchorage hotels, and you won't need a rental car.

Or (same plane) stop in Nome, the historic gold rush town on the Bering Sea. If you're really feeling adventurous, rent a car and drive out across the Seward Peninsula to Teller, probably passing muskoxen and maybe some bears in the process.

No shortage of options.