We spent 3 nights in the area in September of 2018. We really wanted to try some areas outside of the RS books, and stubai was one of our picks. We stayed at this B&B:
We loved our time there. Our host gave us Stubai cards that allowed us to ride buses, lifts, etc for free. We hiked up Elfers, rode the lift up to the Stubai Glacier, Went on the Rodelbahn that was up the Serles lift and had a great time. (the Rodelbahn was also free with our pass) Here is a video:
I have ridden several of these Rodelbahns, and this one was the best I've been on.
Here is another video that inspired us to climb Elfers:
It is in German, but the scenery speaks for itself. We did climb all the way up to the official top of the needles, but the great thing is that a lift takes you up high enough to enjoy the views without hiking. There are many walks from the top of the lifts as well. If you are up to it, there is a shorter but steep climb to the Elfers Hutte which wins my "hut with fantastic views and food" award.
Stubai Glacier is a long lift that takes you right up to the glacier. There is a restaurant at the top as well.
i think this area is worth visiting for the length of time you have. We had a car, so I can't comment personally on public transportation. However, I believe there is a train that goes from Innsbruck to the area. You would need an accommodation with walking distance of the train station. I used this web site to book Haus Wally:
Not all places offer the Stubai card. I do think it is worth paying a little more for one that does. It saves so much money on all the lifts and public transportation. Here is a list of what is included:
It looks like it includes both a bus and a train that runs between Innsbruck and this area Of course, things may change when everything opens up. We just have to wait and see. FYI- we were 62 during our visit, but we are avid hikers. We would love to return for another visit.