Since you're arriving May 13th, Denali is out because the shuttle buses don't start running until May 20th (http://www.nps.gov/dena/planyourvisit/hours.htm).

You may want to go to Anchorage, rent a car and head to the Kenai Penisula ... personally I'd drive all the way to Homer and stay there for a couple of days before heading back to Anchorage. (look at this) But I'm partial to Homer.

Another option might be to fly to Fairbanks, rent a car, and head out the Chena Hot Springs road ... we've seen moose, eagles, wolves, etc., on our way to the springs many times. It's been pretty warm in F'banks the past few days so the snow is melting fast, and the birds are landing at Creamer's Field on their migratory runs to the Arctic. You're bound to see quite a bit of birds at Creamer's Field, and it's easy to get to (taxi, city bus, or rental car).