Best area for hotel or Airbnb in Innsbruck, Salzburg and Vienna

Anywhere in the center city of either Innsbruck or Salzburg would be fine as they're both very walkable cities. It's been awhile since we've visited there so we have no names of properties for you. Both are cities where any property you stay in will be just fine--no matter the price. See Booking.com.
For Vienna, we always stay where Rick Steves used to stay--K&T Boardinghouse. The rooms are huge, it's incredibly clean and a metro station is 50' across the street. It's only one metro stop outside the ring--5 minutes to everything. Rooms are 79 Euros for two people. See KTBoardinghouse.at/en

In Vienna it is most important to have fast access to public transport, which is very easy to use and widely available. You cannot visit all sights just by walking, at least not in a reasonable time.

Relations of my wife and myself stayed already multiple times at this place:
https://www.airbnb.com/rooms/1027443
It is spacious, fully equipped, extremely clean, and has excellent connections to public transport.
(It is for two people, only.)

In Innsbruck we stayed at the Austria Trend Hotel Congress - not in a bad spot - right by the river and we had some nice views - buses close by but we walked to the downtown in about 10-15 min. I was just looking for something within our budget and it was a nice hotel.

In Vienna we stayed at an airbnb near Burggasse-Stadthalle metro stop - it was a few blocks up - tram just outside the door and we'd be at Museumquartier within 10 min. You can stay around the edges of the city, just make sure you are near a tram or metro. If you're interested in the airbnb lmk. It was a private room with the owners present, but you had your own bathroom, access to the kitchen (they laid out a small breakfast for us, and she made an amazing apple strudel the morning we left) and they even let us use the washer. Beautiful converted flat (2 combined) with amazing high ceilings, elevator and lots of food options nearby. I don't think they rent out all the time though.

What area of Vienna to explore by foot? The first district or Innere Stadt as it indicated on the Airbnb website. Landstrasse (3rd), Wieden (4th), Mariahilf (6th), Neubau (7th) and Josefstadt (8th) are all good areas as they are convenient to the center and are attractive/have restaurants, etc, particularly the areas closest to the Ring (avoid the Gurtel, the outer ring).

Are you willing to stay outside the Ring and touristy area? If so, you might consider: https://www.marriott.com/hotels/travel/viefg-courtyard-vienna-prater-messe/

We used Marriott points at this Courtyard; modern, clean, nicer we thought than most US Courtyards. It's near the University and the Prater; quiet, safe neighborhood. Public transportation is excellent in Vienna and we were just a block or so from the U-Bahn station. The ride to town was 15 minutes or so as I recall.

Thanks everyone for the responses. I will read through them all after work today to finalize plans.

We stayed at this AirBnB in Wien last October
https://www.airbnb.com/rooms/22030405
Highly recommended. Great location--actual address is: Marc-Aurel-Straße 2b, Innere Stadt, 1010 Vienna

If you don't mind paying a little more, the Steigenberger Hotel Herrenhof is right around the corner from the Hofburg. Most of the major sites are within walking distance (and the Hofburg is almost within spitting distance). This is somewhat of a higher tier chain of hotels, but I've had nothing but excellent experiences with them.

I've stayed at the Hilton in Innsbruck many times. Great location and splendid hotel. There is a BubblePoint laundry not far away, near the train station. In Vienna, Pension Kraml is outside of the ring but still within walking distance. They are excellent hosts. I checked several AirBnB's for my trip to Salzburg this year but found none that I particularly cared for - either for price, location or amenities. I hope you find some to your liking.