Innsbruck is a beautiful city with a rich history and culture. Here's an ideal itinerary for 7 days in Innsbruck:

Day 1: Arrival and City Tour

Upon arrival, take some time to settle in and get familiar with your surroundings. In the afternoon, take a city tour to get a feel for the city. Visit the Golden Roof, the Imperial Palace, and the Hofkirche. Take a stroll through the Old Town and enjoy the beautiful architecture.

Day 2: Nordkette Cable Car and Alpine Zoo

Take the Nordkette Cable Car up to the top of the mountain for breathtaking views of the city and the surrounding Alps. Afterward, visit the Alpine Zoo, which is home to over 2,000 animals from the Alpine region.

Day 3: Swarovski Crystal Worlds and Ambras Castle

Visit the Swarovski Crystal Worlds, a unique museum dedicated to the art of crystal. Afterward, head to Ambras Castle, a beautiful Renaissance castle with stunning gardens and art collections.

Day 4: Skiing or Snowboarding

Innsbruck is known for its world-class skiing and snowboarding. Spend the day on the slopes and enjoy the beautiful scenery.

Day 5: Innsbruck Cathedral and Tyrolean Folk Art Museum

Visit the Innsbruck Cathedral, a beautiful Baroque church with stunning frescoes and artwork. Afterward, head to the Tyrolean Folk Art Museum to learn about the region's traditional crafts and culture.

Day 6: Bergisel Ski Jump and Tyrolean State Museum

Visit the Bergisel Ski Jump, which was designed by the famous architect Zaha Hadid. Afterward, head to the Tyrolean State Museum to learn about the history and culture of the region.

Day 7: Day Trip to Salzburg

Take a day trip to Salzburg, the birthplace of Mozart and a beautiful city with stunning architecture and history. Visit the Mirabell Palace and Gardens, the Hohensalzburg Fortress, and the Mozart Birthplace Museum.

I hope this itinerary helps you plan your trip to Innsbruck!