Best option is to book an accommodation in the city center or near the train station.
Here are some options (not a final list, from more expensive to more "budget friendly"):
Stage 12 by Penz: https://www.stage12.at/
Hotel Maximilian Stadthotel: https://www.hotel-maximilian.com/hotel
Hotel Sailer: https://www.sailer-innsbruck.at/
Nala Individuellhotel: https://www.nala-hotel.at/
Hotel Mondschein: https://www.mondschein.at/
Hotel Grauer Bär: https://www.grauer-baer.at/
Basic Hotel Innsbruck: https://www.basic-hotel.at/de
Motel One - Innsbruck Hauptbahnhof: https://www.motel-one.com/de/hotels/innsbruck/hotel-innsbruck/
Ibis Innsbruck - Hauptbahnhof: https://all.accor.com/hotel/5174/index.de.shtml
Meininger Hotel Innsbruck: https://www.meininger-hotels.com/de/hotels/innsbruck/hotel-innsbruck-zentrum/?gad_source=1&gclid=Cj0KCQjwo8S3BhDeARIsAFRmkONN_ycrEtIQlrbHlHghGaxpiLzz678qsYk1_tbSonsuPXhWTUHAzXQaAtdgEALw_wcB
Please reserve your hotel/accommodation on your own!
