If you go to Valdez the end of August plan on having a fair amount of company there. It is the end of Silver Salmon season and the fish will be close to the harbor so the campgrounds can be fairly full. After 20 some years fishing for silvers there I can tell you August and Valdez normally spells rain so yes check the weather. More than one year we have had snow in the Summit lake area bring the boat home from Valdez in late August.
I am probably biased since I live there but don't agree with skipping Fairbanks if you have never been in this area. Good recommendations above on what to see but also as pointed out the tourist destinations and campgrounds are shutting down rapidly by Labor Day. That time of year is fall here not summer, colors will be changing and areas around Fairbanks will probably have had a frost by then.