As per The Flight Deal, Alaska Airlines is offering LAX-ANC-LAX for as low as ~$276 (5.9 cpm) round-trip in August. Travel up until November is also consistently $296, which is still a decent deal, in my opinion, especially for those seeking an escape to the outdoors and a cheap getaway to see the Aurora.
Anchorage offers a variety of different activities and close-by escapes. Day trips to the Exit Glacier/Harding Icefield Trail and Kenai Fjords are feasible. It's also a great take off point to Denali National Park, home to North America's highest mountain – Mt. McKinley. In Anchorage itself, there's a plethora of outdoor activities that can be done – hiking, scenic flights, rafting, mountain biking, etc. When the midnight sun starts to fade, the Aurora Borealis starts to emerge starting mid to late September. Though some say it can't be seen as far south as Anchorage, find a place away from the city lights. Depending on how far you want to go, a drive up the Glenn Highway, or to Talkeetna, or even Denali South will yield some results. That's enough reason to come sample some reindeer, witness the street-wandering moose, and learn about Alaskan Native heritage.