I lived there for 4 years and loved it. I'd definitely get a car as Anchorage is very sprawling and the bus service is not great.

Some things to do - head down to Girdwood and Portage Glacier for some nature photography. Girdwood is a cute little ski town and a nice place to stop for lunch. Chair 5 is popular with the locals and does good burgers, etc. The drive south along Cook Inlet is absolutely stunning - it's one of the most scenic highways I've seen anywhere. I don't know what the road conditions will be like, but the Seward Highway is well traveled. It can get slick sometimes so be careful, of course.

Seward might be a bit far if you are definite on wanting to stay in Anchorage, but if you decide to make the trip, the Alaska SeaLife Center is excellent.

The Anchorage Museum of History and Art is also worth a visit - link is www.anchoragemuseum.org/

Have fun!