Tom recovering from our first ever hike together.
90 Plus Short Walks Around Juneau is a classic book. Wish I could find mine!
Here's a good site for a sampling of day hikes.
Perseverance Trail, behind downtown, is easy to access and leads into a valley that's beautiful in any weather. Good spot for a run or a mountain bike ride, too. Access by Basin Road, itself a nice walk if you're hanging out downtown.
And as we mention in the "Creature Comforts" section, the Mt. Roberts trail is accessible from Basin Road. Can be mucky, but you can hike up, get a couple of beers or some food up top, then show your receipt to take the tram down.
There are many public use cabins in the area. You might find one available during your stay. Forest Service cabins and shelters may be reserved here: https://www.reserveamerica.com/
The link for state cabin reservations is here: http://dnr.alaska.gov/parks/cabins/south.htm
Here's a cool site that lists al the Juneau area cabins with links to availablity calendars: https://www.alaskacabincalendar.com/Juneau
Finally, if you're on Facebook, you might join and search "Juneau Public Cabin Swep"