Anchorage is the portal to Alaska. Although there are wonderful things to do and see in Anchorage I suggest heading either North or South as soon as possible.
To the north you can head by car or train to Denali National Park. There are flightseeing trips around the mountain available from Talkeetna that would be a highlight of any trip. If you head farther north to Fairbanks be sure to go one more hour north to Cheena Hot Springs. There are many places to stop along the way to hike, bike, and explore.
To the south there is fishing, boating, kayaking, more hiking, and much more. Seward and the Kenai Peninsula are popular destinations. Be sure to take advantage of a glacier tour through one of the many tour boat companies. You will not be disapointed. There are fishing and rafting opportunitites on the Kenai River. Out of Homer guided fishing boats can take you out for a halibut fishing trip.
I just spent 10 days on the Kenai Pennisula and there are not enough words to describe how beautiful it was. We did a day cruise out of Seward and the wildlife we were able to see was amazing. We also hiked into a Forest Service cabin for a couple of nights and it was the hightlight of the trip. We were able to see an abundance of wildlife in a remote part of alaska. If you are into the outdoors I would highly recommand this option for part of your trip. Alaska is absolutly beautiful and I can't wait to get back!! If you go to Seward do not stay at Miller's Landing!! It is a very crowded and unkempt campground.
North, South, it doesn't matter. I've been from Delta Junction down to Wrangell and just about all points in between and have never NEVER been disappointed or disillusioned with anything in Alaska. If you're going down the Al-Can highway and need a place to stay, Helga will welcome you to the Off The Road House International Friendship House B & B with shiny angels in the windows. The best hamburger I've ever eaten was in Mentasta at a place I think was called the Mentasta lodge, right off the highway - can't miss it, it's the place with all the burl wood and diamond willow out front of the store next door. Gwynn's in Cooper's Landing welcomed my cousin and I at 6 in the morning when I tried to drive from Tok to Kenai on 2 hours of sleep (salmon chowder makes everything better). The kind (and attractive) crabbers gave us four clusters they boiled that morning after we took a dip in the hot springs when we stopped for the night by a big waterfall on Baranoff. The sealion left me a head near Sitka (he swallowed the rest of my 40lb king whole). We watched humpbacks teaching their babies to dive near Kake, caught a 20-armed starfish, and saw "migrating flamingos" on the way from Kake to Sitka. We were lucky enough to watch a cloud-free Denali shine in the sun for 4 days before flying over it in fear and awe. That's not half of what we've seen and we haven't seen the half of it. There's SO MUCH to see and do and all the people we've met are not just the most hospitable, but the friendliest people! Now I've got to stop before I get carried away.
We plan on starting in the south (Haines), and riding our Harleys up through Anchorage, Fairbanks, then up to the Artic Circle. I can't wait to see it all. I'll be journaling, and sending pictures to my friends and students in Florida the whole time, via the internet. I also hope to post our adventures to this website.