The hours of operation of stores in Innsbruck were a lot shorter than what I am used to here....a city that never sleeps, N.Y.C.
Stores will close around 5pm-6pm...plus they have longer lunch time hours. Don't take grocery stores for granted either because they close around 6ish also.
What to buy: There are enough grocery stores that you can find necessities.
There are a lot of specialty stores that sell cheeses (very strong smell as soon as you walk in the doors), wines, other ethnic gourmet foods.
Buy or rent any snow gear in town, or plenty of shops on the mountain.
What to pay: Prices were reasonable.
Specialty foods will be a little more expensive, but you're going to be paying for quality and freshness
Be careful when you want to go shopping. Shops close at 6 p.m. on weekdays and on 12 even on Saturdays. Sundays they are closed. We wanted to do some shopping on our last (early) evening and the only thing we found everywhere was closed doors!
Most stores are open from 8:00 or 9:00 a.m. to around 6:00 p.m., with a one or two-hour lunch break, Monday through Friday, and 8:00 a.m. to 12:00 noon or 1:00 p.m. on Saturday (Saturday afternoon shopping to 5:00 p.m. only every first Saturday of the month).
Hours tend to differ in resort areas, with longer lunch breaks but weekend openings. Check the hours for those stores you are interested in! U.S. traveller's checks are widely accepted in Austria.
Don't forget to keep your receipts to get a refund back on the tax paid, at the border when you leave Austria.