These are all excellent suggestions! As an Anchorage resident, my primary place to play is in the Chugach between Anchorage, Eagle River, and Girdwood (it's a big, wonderful triangle), but I have a special place in my heart for the Lost Lake trail and Caines Head down in Seward. The Lost Lake trail is the most beautifully crafted trail I personally have seen, and the scenery is also excellent. I circumnavigated the lake in a snowstorm last October, and I just love the place. I dream of hiking up there and bushwhacking down Martin Creek to the Resurrection River trail out from Exit Glacier. It's not uncommon for folks to hike from one TH (Lost Lake, Primrose) to the other and then hitch back to their cars.
Caines Head is a fun hike out to the beaches, but if you want to see some scenic sights that will 'splode your cerebellum go up the Alpine Trail. You get an extraordinary view of a bunch of forested islands, and also a great view of the valley going behind the mountains. I went up there once, briefly, in 2011, and I've wanted to go back ever since, and bring friends to share it with. Also, even up the Alpine trail is only like 5-6 miles, I think, though timing things with the tide can be a touch tricky.
Hope this helps!