I don't know how old your kids are, but an outdoor kid friendly activity your whole family can enjoy is the disc golf course in Westchester Lagoon. You'd have a pretty good chance of seeing a moose while you play. I also like to wander around at the end of the airport runway and watch the planes take off from the beach. Renting bikes and tooling along the coastal trail would be another fun activity for the whole fam, with an added bonus of great scenery. You can start that from down town.

Here's a couple of websites:

http://www.dnr.state.ak.us/parks/akt...c/knowlsct.htm

http://www.trailsofanchorage.com/