For scenery, it's hard to beat the Glenn from Anchorage to Glennallen in either late spring or late fall. Fairly scenic in summer as well but for summer scenery, my personal favorites are the Richardson down to Valdez and the Denali Highway (Paxson to Cantwell) but the Denali is likely off limits in a rental.
Agree with the previous comment re: McCarthy: The Wrangells / Wrangell-St. Elias is spectacular, but save the time and wear and just book a flightseeing trip from Chitina. The drive to McCarthy is getting better, but is not terribly scenic.
I really like the drive to Seward (and/or short trip to Whittier) but, other than as a way to get to some fishing, the KP has never quite turned the crank for me. Similarly, my head knows that Hatcher's Pass is scenic, but I'd rather drive to Eureka and have a cuppa and a slice of pie.
There are some sights to see in Fairbanks, but perhaps not too much wildlife unless you head out of the city.