Hiking...

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Flattop (Anchorage)
Great views of the Chugach mountains; some scrambling up rocks towards the top of the trail. 
Round trip:  3 miles
Elevation gain:  1252 feet
High point:  3510 feet.

Rendezvous Peak - Arctic Valley (Anchorage)
Relatively easy, steady, uphill climb.  Great views from the pass at 3468 feet as well as the peak.
Round trip:  3.5 miles
Elevation gain:  1500 feet
High point:  4050 feet

Winner Creek Gorge - (Girdwood)
Easy, flat hike through the forest at the base of Mt. Alyeska.  Hand tram over the gorge.
Round trip:  5.5 miles
Elevation gain:  260 feet
High point:  600 feet

Bird Ridge - (Anchorage)
Steep hike offering great views of Turnagain Arm.
Round trip:  2-12 miles
Elevation gain:  4600 feet
High point:  4650 feet

Wolverine - (Anchorage)
Steep hike with views of the Alaska Range.
Round trip:  11 miles
Elevation gain:  3340 feet
High point:  4455 feet

Trails of Anchorage
Anchorage's parks offer many great walking, biking, and skiing trails as well.  The Coastal Trail is especially popular.  See the above link for details.