In June the days are the longest (about 20 hours of light) and the voracious Alaskan mosquitoes are out. These things are HUGE and they will chase you through the woods. By August, the mosquitoes are gone, and days are shorter but it's still summer.
Denali is beautiful. From the park road, it's a very expansive landscape. The distances are great and long lens will allow some very unusual telephoto landscapes with flattened perspective and, most likely, some atmospheric haze and other effects. The attached photo is near polychrome pass with a 135mm lens on a Canon D60.
If you want to stay closer to urban areas, some time in the Matanuska-Susitna valley near Anchorage is well spent. The photo is the Little Susitna river in the Mat-Su valley.
Enjoy your trip.