In town:
Alaska Aviation Museum
http://www.alaskaairmuseum.org/

Downtown Museum
http://www.anchoragemuseum.org/

Alaska Native Heritage Center
http://www.alaskanative.net/

Alaska Zoo
http://www.alaskazoo.org/

Walk along the Coastal Trial, past the airport to Kincaid Park
2009 Foraker Dr, Anchorage, AK 99517

Out of town to the south:
Drive down Seward Hwy towards Girdwood, numerous scenic lookout points

Potter Marsh Wildlife Viewing Boardwalk
2999 E 154th Ave, Anchorage, AK 99516

Beluga Point
Mile 110 Seward Hwy, Anchorage, AK 99540

In Girdwood
Check out shops, bakery, restaurants.
Recommend:
http://chairfive.com/
http://www.doublemuskyinn.com/
http://www.thebakeshop.com/

Continue drive south to Whittier thru 2 mi tunnel built during WWII
https://dot.alaska.gov/creg/whittier...schedule.shtml

Continue farther south to Seward (deep water, ice free, cruise ship port)
Alaska Sealife Center
http://www.alaskasealife.org/

Continue driving even farther south to Homer (known as a small drinking village with a fishing problem)
Historic Salty Dawg Saloon
http://saltydawgsaloon.com/

OR, you can drive north to Talkeetna (launching point for Denali air tours, river rafters and mountain climbers)
https://en.wikipedia.org/wiki/Talkeetna,_Alaska