Innsbruck is very well connected and you can reach the city via air, train, bus or car. Innsbruck Kranebitten Airport is the largest airport in Tyrol region and currently regular scheduled flights are available from Vienna and Frankfurt. Regular (direct) trains operate from Venice, Bolzano/Bozen, Zurich, Munich, Graz, Vienna and many other destinations.
We took a Flixbus which costed us only 7 euros per person, one way. The bus dropped us near the Innsbruck Hbf, from where we took public transportation to your Airbnb.