One thing I wanted to do in Alaska was the glacier trek. In Juneau you can go with the tour group Above and Beyond Alaska. It's an 8 hour hike/trek for $199 per person so it's not cheap, but I think it's well worth doing. The hiking bit isn't actually that long but it takes longer because of the rock scrambling and you spend a lot of time on the glacier so the total trip is 8 hours. They'll pick you up at a hotel and provide you with rain gear, a day pack with a bottle or water and snacks, and hiking poles should you need one. Oh, and of course crampons and ice axe for walking on the glacier later. You need to come prepared with your own good hiking shoes, though.
The trek started easy with a flat trail through a temperate rainforest.
One of the reasons you might not want to attempt this trek on your own as a tourist is because the trail changes all the time. When I did the hike the main trail was flooded so we had to do a lot of bush whacking around. This is when you need a local guide!
There was some steep descent on volcanic rock, then some rock scrambling after the forest trail ends.
At the top, you'll finally see Mendenhall glacier! It's about a mile in width and stops at the lake (so, another option as I've found out later is that you can kayak to the glacier via the lake, which would be a lot shorter at 45-60 minutes).
It's time to put on the crampons and walk on the glacier.