Where to stay between Imst and Innsbruck

Seeking help with travel recommendations for Tyrol, Austria. My girlfriend and I (in our mid-20's) are travelling to Tyrol, Austria in August of 2026. We will be hiking the kaunergrat circular route (3 days, 2 nights). This hike begins and ends in Plangeross. We have a full day to spend in the the area before the hike. We are also looking for a place to stay the night we finish the hike, and into the first half of the following day before we catch a train to Vienna.

For logistics, we would prefer to stay in Imst, Innsbruck, or somewhere in-between so that we are not too far from Plangeross. Imst seems to be the closest medium-sized town to Planergross. Although a bit further, Innsbruck is also intriguing. We are traveling on a budget and are looking for inexpensive accomodations. We are interested in experiencing history, art, nature, and anything unique to the area.

Recommendations?

Thanks!