Going by this year, with record heat and massive wildfires, any predictions about summer weather in Alaska are pretty much out the window. The more the seas rise and the arctic ice cap melts, "typical" weather is going to be a moving target. And of course you can't generalize "Alaska weather" when you're talking about, basically, a subcontinent, with umpteen climate zones, from arctic to alpine to coniferous rainforest... Without the "where in Alaska" part, it's pretty meaningless. May might be sunnier than June (on average) in some places, and the reverse in others. And even then, there's no telling - there can be summers when it seems like it rains in Anchorage and the northern Kenai every day, and others when the weather is ideal.
But based on
past performance, here's the deal. Denali is not fully accessible until well into June. The buses start running to the Eielson visitor center (which is the minimum distance I'd suggest) around June 1, and to Wonder Lake a week later. THIS IS NOT SET IN STONE; the park personnel have the authority to adjust things based on road conditions. Here's this year's shuttle schedule -
Attachment 2887 Remember that fewer than half the visitors to Denali actually see the mountain; it's so big that it makes its own weather. So building an itinerary about the presumption that you're going to get those amazing shots of the mountain looming over the tundra - well, good luck.
Within the park, and pretty much everywhere near fresh water in southcentral and interior Alaska, May and June (really until mid-July) is also mosquito season. At Wonder Lake they'll pretty much carry you off. This is less an issue near salt water or in the towns, but worth remembering when it comes to your packing list.
So my recommendation is to start by deciding, maybe in some detail, what you want to see, then do some research on specific destinations (Denali, Sitka and SE Alaska, etc.) to see when on average they're at their best. Much will depend on how long you have; distances are great. I'd also highly recommend thinking about getting off the road system at some point, and at least one airborne experience - you can't grasp the scale of the place from the ground or the deck of a boat.
If it was me - and it's not - I'd personally plan for the end of the summer rather than the beginning if Denali is a priority. Sure, you run the risk of not seeing the mountain, but the odds are not appreciably worse than earlier, and the upside is that autumn comes to the tundra quite early, giving amazing colors and views. The animals, especially the bears, are very active storing up the calories for the winter (as opposed to the spring, when they're just as likely going to be far from the roads.) In other places, like, for example, Seward, the silver salmon are running - best fishing of the year IMO. Also the bugs are generally gone, or at least better, than in earlier in the season. Just as a thought experiment, look at conditions in late August in the various places on your list.
Happy planning!