The Red Dog Saloon in Juneau is the bar that is famous / supposedly the one to go to. It's alright. It's right in front of the docks, so it's hard to miss. The Alaska Brewing Company I believe runs shuttle busses to their facility for a tour. The Alaskan Hotel and Bar is the oldest continuously operating hotel in Alaska. I don't think the bar has the same "pedigree" but it's old/historic, however you view those kinds of things. It was recently renovated and featured on the show Hotel Impossible. Most bars in town are pretty much dives. I wouldn't be terribly upset if I missed them.
If you are up for a hike, you can take the Mount Roberts trail up to (you guessed it) Mt. Roberts. This is the same location that the tram charges a large sum of money to take you up to. From where the tram departs at the base, you hike up Franklin Street (and at the North end, it really is "up"), cross a block over to Gold Street, which dumps into Basin Road. The trailhead is about a mile to a mile and a half from the tram. The trail itself is about 2.5 miles to where the tram ends. It has an elevation gain of about 1800 feet from the bottom of the tram. If you buy lunch at the restaurant, you can get a free ride down. Otherwise the tram costs $33 per adult, $16 for 6-12 year olds round trip. At that point, you can also go up higher to the peak, but then you are looking at a huge portion of your time in Juneau. Hiking up, taking a look around, eating lunch, and taking the tram down can be done in 2-3 hours, depending on fitness.
If you continue on past the trailhead for Mt. Roberts, you can go up Perserverence Trail, which has a mining museum, and some old mining equipment, etc. I don't know how long your stay is in Juneau, but that one is probably a little too far to do comfortably.
You can take a taxi or tour bus to Mendenhall glacier, and hike the half mile out to nugget falls like LESPAUL suggested, or one of the other hiking trails around the area. Salmon won't be in so you can't see the bears eating the fish right next to the trail, but there are some really pretty views. Trail through time is a nice hike that marks out the location of the glacier face through the years. It's interesting to see how far out the glacier was 100 years ago.
If you are adventurous when it comes to food, I really like V's Cellar Door, a Mexican-Korean fusion restaurant. I don't know what day you are getting in, but they have specials on Tuesdays and Thursdays. They might also have a food truck doing halibut tacos by the docks this summer. There's an Indian place called the Saffron which is good too. Seafood is big up here. Tracy's Crab Shack is the standard, and it is expensive, but from what I've heard its worth it if you want king crab legs or crab bisque.
LESPAUL has been here longer than I have, so he'll probably be a better source of info.