The Wrangell-St. Elias National Park is one of the most primitive parks in the world with some stunning scenery that can only be reached by bush planes. Its chief attraction is also its detriment to people like me who can't afford the cost of flying to many of these destinations.
Thankfully, there is Nebesna Road, one of only 2 roads that go into the park. The road itself is rough and potholed but it is worth the time to do the entire road for sightseeing the day before you actually backpack and/or day hike. To decide where to go, your best bet is to get Mr. Kost's book (see above).
My friend and I did the Trail Creek/Lost Creek loop. Unfortunately, it never stopped raining so we never really got a chance to explore. I picked that one because it looked the easiest to navigate. The first and last part of the hike is traveling along the gravel of a braided riverbed.
When we got back from our overnighter, the next day we did a day hike up the Caribou Creek Trail, one of the few trails that are clearly marked. It started raining heavy again, but thankfully there was a dilapidated hut at the end to hang out in till it stopped. At the end is a beautiful valley but the hike itself was nothing to write home about.
After seeing other sites on the road, I hope to come back and do the Volcano Trail where you cross a mountain that's a polychromatic wonder.
Anyway, if you're looking for a real primitive and pristine Alaska experience, and you're on a limited budget, this is a great bet.
This area is for experienced backpackers only! A real knowledge of topo maps and navigation is crucial. In this park, you cannot expect that you will be rescued or found right away. You should hike with at least one other person. A wise person will leave their itinerary with the ranger station at the beginning of the road. I urge you to go to my Education page and make sure you have all the necessary skills covered.
This is definitely mosquito country; bring the DEET.
Be aware that several creeks cross under the road. In heavy rain, they may overflow possibly trapping you in the park until they recede. Pack some extra supplies in your vehicle just in case you have to stay over for a few days.
If you're just camping at one of the great sites off the road, this would be a great place to bike the entire 40 mile road. It's rough, so use a mountain bike.
For more information, I heartily recommend Hiking In Wrangell-St. Elias National Park, 2nd Edition by Danny Kost.
There are several single campsites with their own lakes and outhouses. Get there early so you can claim one for your own.
The drive there from Anchorage is a great road trip. The Glenn Highway is one of the most scenic in America. At mile 100, make the Matanuska Glacier Rest Area your lunch stop. Since the driving time is under 5 hours, take a side trip to Matanuska Glacier where you can actually walk on top of it.