Good place to buy a SIM card near Hotel Goldenen Adler in Innsbruck?

At the Kaufhaus Tyrol in Maria-Theresien-Strasse there is an A1 shop and an electronics shop at the top floor. But I seem to remember other shops in the area. As everywhere in Europe, you can buy a local SIM at good rates for the local network, it will likely work also in other countries but roaming rates will apply.

The Golden Adler is a hotel in the old part of Innsbruck, and you're a very short 2-3 minute walk from the business district. You'll find phone stores there where you could buy a SIM card.
If you have a GSM phone that's unlocked, you can switch to a T Mobile $50 monthly plan that has unlimited worldwide texting with $.20 per minute voice. It works seamlessly with the service in the U.S., and there is no contract. You can cancel the service upon your return home without penalties, etc.
Last time I had a SIM card in Italy, I had problems--and an automated attendant phone number that was only in Italian. I communicate just fine with a 1 pound Chromebook on my hotel's wifi when in Europe.

That T-Mobile idea is feeling good to me.

Unlimited Europe data also?

I've been using T-Mobile on a couple of trips to Europe each year and its been flawless from Istanbul to London and everyplace in-between. Yes, free texts too.

I bought T-Mobile SIMs today using the Simple Choice plan in the States for my phone and iPad.

Question: which phone do you think would work better? I put it in my Dad's old Verizon iPhone 5 hoping for LTE but now see the bands might be different as far as LTE in US and Europe.

I also have an old iPhone 4 from AT&T I have used on other European travel. Both are unlocked.

Right now I'm getting lots of EDGE and occasional 4G in the States with the Verizon iPhone 5.

I might take both and just see which works better.