You really don't want to hit Fairbanks before mid June. May is Break-up! You don't want to see or drive in that. June can be good for wildlife viewing because the trees are mostly still bare, but it's still frosty early in the month with snows many years. Yeah they only last 2-3 days, but if you are there those 2-3 days...well, it's like winter down here. Try to hit solstice, you'll never forget it.
Maybe better to see the Kenai in June than Fairbanks, much more hospitable weather. Even mid May would be possible on the Kenai.