Hike or take the air tram from Seegrube to Hafelekarspitze (2334 m) from where you enjoy a wonderful sight over the valleys into the mountains surrounding Innsbruck.
In wintertime this is also a very steep downhill.
Equipment: It's alpine district so wear very good shoes
Instead of taking the cable car from Alpenzoo to Seegrube you can also hike. It's a very well marked path over the alps and not very steep, but you have to take your time.
You get a wonderful sight over the city of Innsbruck
Equipment: Good shoes and enough water are a must