I think the lack of responses so far may be because the first week of May is such a difficult time to advise about. It's a little like heading off into the Colorado 14ers in early May ... there's a whole range of challenges, starting with the fact that most trails are buried. You say no river crossings ... what if they are still frozen? Some will be.
In Juneau, a few trees at sea level may just be starting to leaf out but I imagine there will be massive snow loads on pretty much everything above 500 or 1000 feet. Kayaking might be your best bet there.
Up here around Anchorage, I am dying to tell you it will be spring by then because I want it so badly, but just yesterday we got another 8" of snow at sea level, more on the mountains. I think you will be too early for one standard, well-developed trail that people like to backpack, the Crow Pass crossing (avy danger, river issues). Other nearby classics like the Lost Lake Trail will likewise be so deeply buried you might as well be off trail. The Resurrection Pass trail might have a reasonable ski/boot track to follow. Here are a few other ideas:
1. Look on my page here: http://www.summitpost.org/mountain/rock/566512/Mt-Magnificent.html
. The ridge to Mt. Magnificent is a good early season hike and I've done some fun camping up there in April/May. It's hard to get lost, and it's very easy to access from Anchorage. The lower ridge will be like this: http://www.summitpost.org/view_object.php?object_id=285276&context_id=566512
. The upper ridge will be entirely snowy. You'll reach a good summit for sure, but the actual tippy top might be a little scary, depending on conditions the day you go.
2. A local springtime standard is Gunsight Mountain, located about 120 miles east of here on the road to Glenallen. Get a copy of 55 Ways to the Wilderness in Southcentral Alaska and follow the directions there. The mountain can certainly be done in a day, but snow camping on a bench about a thousand feet up the ridge can be a real treat, and then you dayhike the south peak from there. Bring snowshoes at least; sometimes crampons might help a bit at the top, but it's not steep.
3. Some of the main valleys accessed by the Glen Alps trailhead in Anchorage will be at least partly hikeable by then, although you'll certainly want skis/snowshoes. The heads of the valleys can have avalanche issues, but you should be ok if you stay well away from the steep chutes and headwalls. Again, 55 Ways would give you basic info.
4. One local hiking peak that is quite exciting, Rainbow, will be completely snow free then. PM me if you want info. It's not really a place to camp, though.
Steve Gruhn will see this and add other ideas.