>>833725>No equipmentI assume this means you have at least hiking shoes and rain gear/warm clothes (i.e. a hardshell/softshell jacket and some fleece pullover).
Check out Grünausee (
>>833055), or the High Moor behind Neue Regensburger Hütte. Both in Stubai Valley (if you don't have a car, you can reach it by bus).
Both about 800m ascent, and doable with halfway decent hiking shoes. Achselboden over Innsbruck is nice too.
Gleirschklamm (from Scharnitz) is very beautiful too. Reachable by train from Innsbruck.
If you want to take a cable car, go to Hafelekar over Innsbruck and walk to Pfeishütte.
I also heard that Solsteinhaus (Train from Innsbruck to Hochzirl) has pretty good food, so that's worth checking out, too.
For shitty days, check out the Ferdinandeum Museum in Innsbruck. They currently have a exhibition about portraits which is very nice.
You should find all the information you need on the internet. Specifically
alpenvereinaktiv.com should have all you need.