How much money ya got?
I'm half joking there, but Alaska can get pretty expensive. It depends on how crazy you want to get. Here are my favorites in order:
1. Katmai: this is in my top 2 outdoor experiences of all time. Mathguy nailed it by suggesting Brooks Lodge, so plan ahead. If you can't book a room there, try to get a camping permit or do a fly-in day trip. No matter what, you're flying into the park. Watching the bears at the falls is incredible. And walking past bears on the trail is incredibly nerve racking!!!! Be sure to look both ways when leaving your cabin, too. Bears are everywhere!!!
2. Wrangell: we stayed in a private house in McCarthy and used St Elias Alpine Guides for our excursions. We did ice climbing one day on the glacier and ice caving the second day. Then we had them fly us out to a remote iceberg lake and camped for two nights. You can also pack raft down the river and camp, but we didn't have time for that adventure on this vacation. We drove most of the way from Anchorage and then flew in the last main section of road to save time. I think this park is number 2 on my list because we got off the beaten path and had that iceberg lake (and probably another 100 square miles) to ourselves. Otherwise, Kenai may have jumped it, but I'm splitting hairs there. Do both!
3. Kenai Fjords: I'm not a cruise guy so I would never do a multi day cruise up the coast, but that said, I am a boat guy. We used Major Marine tours for a 10 hour tour out to the glaciers and to see the wildlife out in the Gulf. It's a long day but it's awesome. We've actually done it three times now. There is some good hiking near the visitor center in the park, which is about 15 minutes from Seward. The aquarium in Seward is worth a visit. Do the private octopus experience, which needs to be booked way in advance. We've stayed in town and at the Windsong hotel. I like the Windsong better, as it feels quieter. And it's only a few minutes from town. The drive from Anchorage to Seward is beautiful. Stop at the Alaska Wildlife Center about halfway down.
4. Lake Clark: we stayed at Redoubt Mountain Lodge and it was pretty awesome. We mainly fished (had a guide for 8-10 hours a day) and watched bears. This was before my Katmai trip and it was my first experience with brown bears. It was ranked higher up until we went to Katmai. That said, it's beautiful there and I'd love to go back. There were only lodge guests (8 other people) so it was quiet. Fishing was fun because we'd be in waders right off the bank and we'd see a bear coming so we'd hop in the boat, motor out a few yards, and then wait for the bear to pass before heading back over. There are other areas of the park which are considerably cheaper. Like Katmai, you'll need to fly in from Anchorage.
5. Denali: we went before the rock slide so we're able to get all the way to the end of the road and stayed a few days at Backcountry Lodge. It was 2020 so our bus ride out there only had 2 other people on it. It was like a private tour. Good wildlife viewing on the ride out. And it's a beautiful scenic drive. We saw dall sheep, caribou, moose, bear, beaver, and porcupines. We hiked at 10:30pm at night which was cool. Didn't see Denali from the park but took a plane ride out of Talkeetna and saw the peak for a few seconds. Landed on a glacier along the mountain and had a snowball fight.
6. Glacier Bay: we flew out of Juneau on Alaska Air and landed in Gustavus and stayed at the lodge in the park (about 10 minutes from "downtown"). It's about a 17 minute flight to get there so I spurged $20 so my son could fly first class for the first time. We did a day tour on the park's boat which gets you in closer than the larger cruise ships. There's a little hiking inside the park and you can rent kayaks, but you're nowhere near glaciers there so it's typical coastal kayaking. Not much to do in Gustavus, so we fished for a day.
7. Kobuk Valley: the goal was to camp and fish with local guide out of a small village but that fell through so we chartered a plane out of Kotzebue to take us to the sand dunes. It was pretty cool but I'd only do it if you're on a mission to see all the parks.
8. Gates of the Arctic: my goal was to backpack there but like Kobuk, life got in the way. So we made it to Bettles with the intent of doing some flight seeing and a little fishing. But then weather got in the way and we only made it barely inside the park along the river. My report is pretty incomplete on this park.
Pages 12, 14, and 15 on the Favorite National Park thread have a few post about Alaska from Ryan, Mathguy, and me.