How active do you want to be? I might recommend rather than just seeing a glacier close up that you consider a glacier hike. I did one a couple of years ago and it was great. One option is Seward with Exit Glacier Guides. One of these departs at 11am and takes about 6 hours total. Cost is $125 plus tax.
Another option is to drive north of Anchorage to Matanuska Glacier and do the glacier hiking there. It is a shorter hike (3 hours) and costs $70 plus a glacier access fee ($15 I think). It is about 2 hours northeast of Anchorage (Seward is 2+ hours south of Anchorage). Mica and Nova Guides operate these tours.
I have not done any of these - the one I did was in Wrangell/St. Elias NP. But I have heard really good things about all three of these companies.
Another option is white water rafting near Hope (about 1-1/2 hours or so south of Anchorage). Some Class IV and V whitewater, also operated by Nova.
Just some more ideas in addition to the ones Gardyloo gave above.