The drive from Anchorage to Girdwood (and continuing to Portage Lake) along the Seward highway is breathtaking for landscapes. They are 'easy' shots though—meaning pullouts along the road. If you feel like getting out a bit more, you can drive up to the Glenn Alps trailhead right on the edge of town. From there various routes take you up and around the mountains. The parking lot area also has nice views looking down on the city. Another option is to drive up the Glenn Highway, turn off at Eagle River, and head toward the Eagle River Nature Center. The nature center area has some good and fairly easy hiking and a fair chance of wildlife. If you continue along the Glenn Highway instead of turning off at Eagle River you will hit the turn off for Eklutna Lake which is very scenic. It has hikes along the lake and also up the adjacent mountains.
If you don't mind spending some money, the flight-seeing around Anchorage in the Chugach mountains is amazing. Very dramatic scenery, but very weather dependent.
Enjoy your trip.