Yeah you will be a little late for the Kings and too early for the Clearwater Silvers. I would suggest hitting on of the big lake between Fairbanks and Delta Junction (Chena,Harding, Birch, Quartz). Most people just use bobbers and worms. Theres always the Chena River, you have a good chance of catching some Grayling in there. Dry flies if you fly fish, and small spinners if you dont.
I will be in Fairbanks for 2 days (7/2-4), and am looking for any suggestions as to where I can wet a line for a few hours. Might also have my young son with me so looking for place where he might hook a few.