First of all, I'd recommend a map. You need to drive north to Denali and Fairbanks from Anchorage and the drive is long. North Pole is just south of Fairbanks and the ride between North Pole and Valdez is gorgeous., but again is very long. Denali is an 8 hour bus ride and Mt. McKinley is rarely visible.
You may appreciate the state of Alaska more from the water. You see a lot more of it's beauty. If you are on a shoestring budget, you might consider a trip on the Alaska Marine Highway system. You can sleep on the deck in your own tent and bring your own food (oatmeal, cup of soup). The Inside Passage is a nice route. Valdez to Whittier is also beautiful and the captain will stop for observing whales if they are present.
The Alaska Railroad is also a nice way to travel. Whatever you do, I'd think about more time. 3 days is too short. It takes at least 1 day of travel each direction and the state is very large.
You also may want to consider 1 destination during a good Festival time. February offers Fur Rendezvous. March is the Iditarod. There are fishing derbies and the State Fair in the summer. Lots of other fun festivals, etc.