Trip recap:
The road that runs through Denali National Park can only be accessed by the park operated shuttle, but you can disembark from the bus at any point to start your day hike/backpacking journey. There are few trails deep in the park and exploration usually requires forging your own path. We asked the driver to drop us off at the east boundary of the Upper East Fork unit (green star below).
First, descend directly to the river that is visible from the road. Follow the river south for about a mile to make sure you avoid the wildlife protection region (red area in the map above) and be prepared for a lot of bushwacking (I think we averaged about 1 mile per hour for the first two miles due to the thick brush in many places).
After passing the wildlife zone, start heading southwest up the tundra. We were there in late May so we still enocountered some large snowfields to traverse.
Amazing 360 panoramas await at the top of the plateau, including views of the distant Denali peak on a clear day with some early-blooming wildflowers to be found amongst the rocks and lichen.
From here you can continue to traverse south towards some of the bigger foothills. The orange star on the map was about as far as we felt like going in a single day knowing we had a long bushwack back to the road.