We will be spending a week "on our own" in Alaska after our cruise this summer and are trying to decide between renting a car and using public transport between Seward, Denali, Fairbanks and Anchorage (in that order). While train and bus travel would allow us to look out the window at the scenery more comfortably, we would have to deal with the limited schedules and also with transporting and storing our luggage each day. Does anyone have any experience that will help us with these issues?

Between those destinations you could go by train all the way. You could walk around most places you want to see in Seward, buses do a tolerable job in Anchorage, and shuttle buses get you around Denali, but public transport is poor in Fairbanks and the place is pretty spread out.

You could probably rent a car for much the same price as the train and you would have more flexibility, though travelling by train is nice.

Your call really. How about getting the train to Anchorage, sightseeing a bit there, then renting a car for the rest. I assume you're flying out of A.