Which of these hotels in Salzburg??

Did you look at hotel Elephant? It is in the center for reasonable price and we were very satisfied with that choice. Unfortunately I did not stay in hotels you are searching.

We have always stayed in B&B's in Salzburg--one of which was on a working farm 4 miles south. Virtually every accommodation in that city and the region will be very clean and a decent place to stay in.
When in doubt, go for the cheapest.

We stayed at the Hotel Mozart at Franz-Josef-Straße 27 for several days February 2014 and were very satisfied. Our room was very large in comparison to our usual European experience and the staff accommodating and friendly. http://www.hotelissimo.de/hotels-international/us/hotelinformation.html

Location is central, being only several blocks from the Linzer Gasse pedestrian only street leading to Old Town. (I believe that Hotel Krone is located on Linzer Gasse) and closer to Der Alter Fuchs Gasthof. Hotel Mozart is closer to the central train station (about a 1 km walk) than the Krone. You can also take a bus from the airport, but we had a ski bag and took a taxi at a low enough cost that it was unmemorable.

The breakfast at the Hotel Mozart was very good including fresh fruit in the middle of winter, a good selection of breads and baked goods along with quality coffee. I recommend taking the hotel's breakfast.

Hotel Elefant is slightly pricier than those hotels. Slightly out of my budget. Shall consider Hotel Mozart then

I've stayed at Hotel Krone 1512 a couple of times, most recently in September. It's a bit of an older property but clean and nicely maintained and I found it to be very comfortable. It's also in a very convenient location.

We stayed at the Hotel Star Inn for 3 nights, decent size room, just through the underpass behind the old city. Easy walk to everything and close to bus routes. Nothing fancy but was very clean, didnt seem dated if I redmember correctly, friendly staff, good breakfast buffet and we had a balcony. Not much of a view but nice to have nonetheless. We tend to spend very little time in rooms when travelling so not really interested in lots of bells and whistles.

I found the Hotel Mozart from the brochure requested from the Salzburg TI resource Perry mentions. Keep in mind that the Austrian Hotel "star" system categorizes hotels by features and/or services and not necessarily by the quality of those features/services.

http://www.hotelstars.eu/

Hospitality Europe, the hotels associations of Austria, Czech
Republic, Germany, Hungary, Netherlands, Sweden and Switzerland have
created the Hotelstars Union. In the meantime, the following countries
joined the star family: Estonia (2011), Latvia (2011), Lithuania
(2011), Luxembourg (2011), Malta (2012), Belgium (2013), Denmark
(2013), Greece (2013) and Liechtenstein (2015).

Their partnership is providing a harmonised hotel classification with
common criteria and procedures in the participating countries.

Explaination of the star system criteria:
http://www.hotelstars.eu/index.php?id=criteria

For example, to be rated as a one star property:

100 % of the rooms with shower/WC or bath tub/WC
Daily room cleaning
100 % of the rooms with TV together with remote control
Table and chair
Soap or body wash at the wash basin
Bath towels
Reception service
Publicly available telephone for guests
Extended breakfast
Beverage offer in the hotel
Deposit possibility