Where to start?
First, investigate the cruises and tours. It shouldn’t be hard to find information. The only thing I can tell you first-hand is that none of my friends or family who have taken a cruise has ever said they were disappointed. Some (most?) of the cruise-line packages include a segment of travel by rail (fantastic views!) and possibly a bus tour of Denali National Park.
Such bus tours may sound dull or superficial, but they’re surprisingly fun. The guides are very informative and entertaining; the views are spectacular; and it takes barely any luck at all to get some great wildlife sightings.
On the other hand, they won’t take you nearly as far into the park as previously. The road fell off the mountain part way in.
I will have to take issue with LSLGuy’s “IMO there is very little of Alaska that isn’t wilderness.” True, there is one heck of a lot of wilderness, but there’s also a lot that’s only - how shall I put it? - wilderness adjacent. Someone who isn’t fond of the back country can still find a lot to do.
There are many remote destinations that are incredible: Katmai (as Chefguy mentioned) the island of Kodiak, the Southeast Panhandle, remote fishing lodges, lots of others. But with a limit to your time, and some differences in your preferences, possibly you’d enjoy the areas on the road system.
Fly into Anchorage. Rent a car or van. Let the hikers choose among day hikes from easy to arduous, while others visit the museum, the tourist shops and the restaurants.
Drive down to Seward, watching for beluga whales (or a bore tide) while you skirt Turnagain Arm (also keeping eyes on the cliffs above for Dall sheep). Watch for moose anywhere you drive.
In Seward pick from a number of day-cruise operators. Anything from a three hour tour (Don’t say it !) to an all-day affair with a lunch stop on an island. Nearly all the visitors I’ve had have called this their favorite part of their trip.
You’ll see an assortment of critters, depending on luck: seals, sea lions, sheep and goats on the rocks above, humpbacks, orcas and other whales.
Lots of bird life - the puffins are favorite, of course, but there are so many others. Once my visitors were faster with their cameras than I was, and they got footage of an eagle flying right freakin’ over us, a salmon in its talons.
And of course watching glaciers calve. Why is it so fascinating to watch chunks of ice fall into water? I don’t know, but it is.
The Sea Life Center is definitely worth a visit, and could be another day when you split up and some go hiking, while some explore the Center and the rest of Seward.
There’s lots else on the Kenai Peninsula, but with Seward behind you (and limited time) you might head back to Anchorage with an eye toward the Mat-Su Valley the next day. But definitely take the little side trip to the Portage Glacier Visitor Center. The Center is mildly interesting, no great shakes. But the drive to it is stupendous, especially on a sunny day when the glaciers above the little valley look so strikingly blue.
Want to see a glacier up close? A day trip further north and east takes you to the Matanuska Glacier. There are guided tours (the safest way) and even the non-hikers in the group will want to do this. The beauty and strangeness of the glacier are beyond description.
The drive to get there is also pretty wild and includes a couple stretches on a twisting, curvy mountain road with a rock wall on one side and a 200-foot drop on the other. It’s not really scary in nice weather (though doing it in heavy snow took at least a year off my life).
Hatcher Pass, a state park in the mountains near Palmer, is a good destination for the next day. It has an interesting little historic site about the history of gold mining in that area. It’s quite well done actually. But the real lure is the abundance of hikes there, from easy rambles to rock-hopping challenges, with beauty everywhere and whistle pigs (hoary marmots) calling on every side of you.
Maybe before you go to Hatchers you can spend a couple/few hours on the Musk Ox farm or the Reindeer Ranch, both near Palmer. They’re tourist traps, but dang appealing anyway, especially (but not only) if you have kids along.
If you’re not sick of driving yet, you could head north to Denali National Park or even Fairbanks. I enjoy Fairbanks, but one visitor put it like this: “nice, but probably the least Alaskan thing we saw.” The city has a lot of history and a museum that is definitely worth a peek. But there’s little else that jumps out at you as being terribly different from a city anywhere in the U.S. And it’s an all-day drive just to get there.
Talkeetna, just a couple hours from Palmer, is generally understood to be what Cicely was based on in “Northern Exposure.” It’s a small town but has a few things worth seeing. The main reason you would go there, however, would be its airport, from which you could get a flight-seeing tour of Denali and the surrounding mountains. When my father visited, that was his favorite part.
I’m rather running on, I think. TLDR: there’s a wealth of interesting stuff to see and do, just in the small portion of the state that you can drive to. Renting a car and designing your own tour could be well worth it.