Some of the best suggestions have already been covered, but I'd chime in that it can be done but you have to be flexible.

Am a huge fan of going in September, for example. Really beautiful then. But: Getting in after Labor Day AND hitting Denali might be hard to do. Places like Anchorage or Fairbanks will be fine, though, and will have some great fall colors.

I remember on my first trip in 1997 that hostels were the only afforable option (for me), but more recently I've gotten some good rooms, especially in ANC, for $30s through Priceline, including a suite once at $37! Many more rooms have come on-line in ANC, and deals are much more possible out-of-season than they used to be. Also got the Westmark in Fairbanks at $55 through PL in September. Outside the cities it's still a matter of a few hostels, some overpriced motels, or camping.

Car rents out of ANC out of season have generally been reasonable with some shopping around, though taxes are much higher than they used to be.

So my typical trip will have ANC or FAI bases and mostly daytrips to spots like the Kenai or glaciers or what-not. You could also do a road-based round-robin with someplace like Valdez as a third base. I also splurged a bit on a $99 Marine Highway RT on the Whittier-Cordova route and vv to see the Prince William Sound glaciers as cheaply as I could.

Don't forget that award tickets to Alaska are only 25K points at saver level, which is another plus for shoulder season. You can find several trips' worth of things to do on fly-drives to ANC (or possibly FAI). Getting to non-road-connected parts of the state (the bush), though, can really run up the expense.