There's much more to do, and places to stay, in and around Anchorage than Fairbanks - do you have any other options?
When I planned our family of four summer trip for 2012, I made most of the reservations the week of 3/2, and pickings were starting to get slim for somewhere to stay near Denali.
Questions other than flights are probably better answered in the Alaska forum - lot's of "what should I do in Alaska" questions there.