What to visit

I’m visiting Innsbruck this week and will be staying for 4 days. I don’t have a fixed itinerary yet, so I was hoping to get some recommendations from people who know the area.

So far, I was planning to explore the city and the Old Town, visit Swarovski Crystal Worlds, spend a day at Achensee Lake, and visit the Alpine Zoo.

If you think any of those places aren’t really worth it or there are better alternatives, please let me know.

I’d also love to hear about any must-see places, hidden gems, scenic viewpoints or nice day trips nearby.

Thanks in advance for any recommendations!