Anchorage in late December with a 7yo
 

My 7yo daughter will need about 5000 miles for UA platinum and we need to fly out of LAX between Christmas and New Year's.

Anchorage seems to be the most reasonable with the other option being IAD or Kansas City (to see the San Diego Chargers play the Chiefs if I can convince the wife). But we have never been to Alaska and it is the cheapest flight of the 3.

I noticed that there are only about 6.5 hours of daylight. Would there be enough time to do something there?

Any recommendations?

What are you interested in doing? It can be brutally cold in December and everything that people come to Alaska for in the summer is shut down. You're basically looking at going shopping at a mall, catching a movie & a bite to eat or going bowling. If you can brave the cold, the Alaska Zoo is open year-round as well as the Alaska Wildlife Conservation Center.

If you're into skiing/snowboarding, Alyeska Resort is about an hour south of Anchorage and is the only ski resort in the state.

It really just depends on what you're looking to do.

The Anchorage Museum is open. That's worth a few hours. They also have a pretty neat built-in science center that would occupy your daughter for awhile. https://www.anchoragemuseum.org/visit/

Otherwise, get a rental car (they're cheap in the winter) and drive around a bit--if you're comfortable driving in winter conditions, that is (they do keep the roads pretty clear). There's some amazing scenery very near Anchorage (head south to Girdwood, where the big ski resort is). Or head out to Kincaid Park and watch the planes land over cross-country skiers. Or join those cross-country skiers!

The "touristy" things might be closed, but don't let anyone tell you there isn't anything to do!

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If ok with the cold (As others stated) the zoo should be fun- and the right night may have some fun Xmas lights up. Also you can always thaw out at the Anchorage Museum- the imaginarium integrated inside inspires the imagination :p