My home state (born and raised)!
Here's a few "musts" for you:
1) The Alcan highway: drive, don't fly. Northern BC/Yukon Territory is the most beautiful area in all of North America. Throw a tent in the car, and while you can do the drive in 5 days non-stop, give yourself two full weeks, and smell the roses. The Lake Muncho area is mind-blowingly beautiful. Whitehorse is a super-hip little town of bohemians. The Liard hotsprings are an experience as well. I can't emphasize this enough -- you have to drive the Alcan!
2) Kenai River / Russian River: if you like fishing, then give yourself 4-5 days in July to get down to the Kenai Peninsula to catch the salmon run (kings, reds, silvers, throw back the chums/dogs and pinks unless it's late in the day and you're getting skunked). There are several campgrounds along these rivers, bring your tent and don't worry too much about the bears -- they won't bother you as long as you don't bother them (pack your pepper spray though, just in case).
3) Homer: stunningly beautiful town, visit it in June/July/August, and you'll think about it for the rest of your life.
That's all I got for now, but PM me if you want more advice/info. Be sure to stop by my home town of Soldotna, go to Sourdough Sals, and have a Yukon Burger for me....