If you are coming to Fairbanks, the 4wt will be perfect for grayling. The Upper Chena River and Delta Clearwater River are really World Class fisheries for grayling. Many fish over 20 inches.
King salmon will be in the lower Chena in July. A 9wt should be good. The kings in the Chena are a bit smaller than other rivers, but still can give you a good battle.
Trout in the Fairbanks area are all stocked hatchery fish in the local pond and sloughs. You can check out the ADF&G web page for a listing of all the stocked fisheries in the Interior. Your looking at,no less than, a 4 hour drive for decent native rainbows. But if you are going to be here for 3 weeks, you might want to take a drive down the Parks Hwy, through Denali National Park, over the Alaska Mtn Range and fish the Parks Hwy streams from Talkeetna to Wasilla.
As always, check regulations before putting a line in the water.

Ben
Fairbanks