I’m planning on travelling in that area (between Skagway and Ketchikan) in late August, early September.
What do I absolutely need to take time to see? What’s overrated? What should I not even bother with?
I used to live in Juneau, but never really did the tourist stuff around there. I’d highly recommend going on a glacier trip, either just a hike around the glacier or one of those helicopter flights that actually take you out on the glacier.
Beyond that, if you like fishing, you won’t find many places better than SE Alaska to do it. 
In Skagway, if it’s anything like I remember it, be aware that most of the shops are very “tourist trap”-ish, so you’re better off shopping in the other towns if you have the choice. Unless you really like kitschy souvenirs. 
The museum in Juneau is cool. Sitka’s kind of cool. Do you like hiking? If you’re into, like, hiking, or fish, or feral camping, or mining history, or eagles, or whales, or bear attacks or glaciers or something I think suggestions would vary.
Take an umbrella.
How much time do you have? What’s your budget like? What are your interests generally? Hiking? Wildlife viewing? Archaeology? Fishing? Hunting?
I grew up in SE Alaska. Feel free to drop me an email if you have specific questions My email should be in my profile.
Are you on a ferry or cruise ship with a set schedule or is your itinerary fairly flexible?
I’ll be there for a little under two weeks. I’m not going on a cruise, but I like ferries.
I don’t fish or hunt, nor do I want to start. I like the outdoors in medium doses, one day in a kayak is great - several days isn’t. I’ll stop at anything that calls itself a museum, and tourist traps don’t bother me.
There is (or was way back in 79) a ferry that went to Haines, which is on the Alcan, it’s a bald eagle sanctuary. VERY cool, the eagles are as thick in the trees as sparrows.
Here are some linkypoos (official sorts)
www.muni.org (to Anchorage, but has other links to Alaska communities and such)
I just came back from Alaska.
In Juneau we could buy a ticket from the tramway office which included transport to Mendelhall Glacier and admission to the museum there where they show you a dinky movie all about glaciers. There was a chunk of glacier ice that you could handle. I’d highly recommend the glacier. The ticket also included a return trip on the tramway. I’m afraid of heights and all there was at the top was a restaurant and gift shop so I wasn’t so impressed with that. Juneau also has a great second hand bookstore and the pizza restaurant in the small mall on the front is excellent as was the smoked salmon from the shop near the tramway.
In Skagway we drove through White Pass (think of all those tough miners!) into the Yukon and saw Emerald Lake and Carcross and Carcross Desert. The Carcross visitor centre has a little museum. Nothing really ‘must see’ there but now we can say we’ve seen the Yukon. Make sure the border guards stamp your passport. There is a narrow guage railway trip from Skagway through the White Pass. I believe it’s quite expensive and the wait at the border is lengthy due to them having to process all the passengers. Personally, if you can’t go all the way into the Yukon, I would at least make it up into White Pass if only to get some sort of idea about what the miners suffered through. There is also the Red Onion saloon bar/ex-brothel. Women dressed as old fashioned good-time girls give tours of the brothel. I was depressed by the effort to gloss over the horror, even the mention of one of the girls hanging herself. The tour would have been otherwise very interesting. There is an excellent little museum of the history of the area in one of the shops in Skagway - requires donation only.
Ketchikan was probably best for tourist shopping. You’ll want to visit Creek Street which is the historic area. Dolly’s House (yet another brothel!) wasn’t as depressing as the Red Onion and if you’re lucky you might catch the rescue bird people there and see a bald headed eagle close up. I know my gold and jewelry and I’d be happy to recommend POKER CREEK GOLD in Creek Street. It’s a largish shop and you can’t miss it - prices seem extremely reasonable. The public library in Ketchikan has a museum which looked great from the outside but we were out of time.
Bon Voyage!
If you’re a wildlife fan, I can recommend the AnAn Bear Observatory - they offer some tours up there from Ketchikan (obligatory link: http://www.alaskavistas.com/Vistas/ANAN%20WEB%20PAGE/Anan%20web%20page.html)
This is my hometown (http://www.wrangell.com) which has a resonable museum, some interesting pteroglyphs, and a whole bunch of assorted activities.
I might check the Alaska Marine Highway schedule listings and plot a possible schedule and then hit the websites for all the cities you’re thinking of visiting. Most if not all of them have museums and various points of interest