Some good suggestions so far.
Having worked in Denali for four summers, and spent much time in the coastal areas, I'll offer my two cents.
Depends a bit on what you want the focus of the trip to be, ie. some people fly up and go straight to Denali for ten days or so, and/or, some focus on the coastal areas.
Imo, why not do both?
Fly into Anchorage, get whatever you need, and get out. Are you renting a vehicle? Or just public transpo? If the latter, train up to Denali, etc. etc.
If you're renting a car, try and reserve(I believe that's the method), a drive-in campsite in Denali, potentially Igloo, and car camp there. Then, day trips to different zones in the park for hiking. Maybe if some are interested, backpack out there for a night.
Others mentioned the "bus ride" in Denali as being not worth it, etc. etc. Imo, the longer you stay in the park, the easier the system becomes. Go for a day and you might not have much fun. One week oughta do it. Day Hikes galore. The last of the American Serengeti. And, the longer you're there, the better your chances of seeing Grizzly, Moose, and the Mountain. The Big Three! Kids going? They'll love it, as will anyone who loves wildlife, hiking, etc. It will be unlike any other place you've been.
Then, with that same rental car, you could head south, day-trip to Homer, Seward and Valdez, car-camping along the way. Take the boat out of Seward to potentially see marine life. Much different than the interior of Alaska. And, agreed, not tons to do in Homer, more so across the bay in Katchemak St. Park, (which would be great for cabin rentals, kayaking, etc. IF you have the time), but even though it's a bit touristy, Homer is still very beautiful, at the end of the peninsula, and worth it, imo. Go Halibut fishing on a boat, if that strikes your fancy.
Do a big loop, head over to Valdez, Seward, etc. then up the highway and back to Anchorage. Not sure of the loop off the top of my head, but, check out the maps and you'll see it. Glenallen, etc. Drop off the car, catch a plane home, and Voila!
This is a trip I hope to do with my son. Hard to do all in such a big, spread-out state, unless one has the time and $$ resources. Getting to Southeast Alaska, which is definitely incredibly scenic, is certainly worthwhile, but, unless you plan carefully, ie, including it in the itinerary by taking the ferry from Bellingham, Wa. up or down(3 days), can be, as mentioned, expensive or time-consuming. You either have to fly down to Juneau, Ketchikan, etc. or, drive down to Haines and hop on the ferry. Driving is a long ways from either Fairbanks or Anchorage. So, you can see, where do you want to spend your time?
Ps. I saw the part of dayhiking. Does this mean no car camping? You could throw the basics in a large duffel, ie. tent and sleeping bags. Have everyone bring their personals, including sleeping mat, in a backpack. Car camping will certainly be much cheaper than paying for lodging.
I think by focusing on the central part of the state, both interior and the coast, one gets a good taste of Alaska fairly inexpensively and easily.
Anyway, lots of good stuff up there! I'm envious! Hope to get up there in the next couple of summers. Say hi to that great place for me.
Pm. me if you'd like with any further questions. I'm no expert, but I traveled around the state for many a summer.