I recently stayed in the same place as mikliz97 (Altstadthotel Weisse Taube) and also can absolutely recommend (we were also 3 adults). The location was great and it was comfortable and charming and very reasonable compared to other Salzburg options within easy walking to the center.
I did not have breakfast included, which seemed pricy. Instead we walked around the corner to the Cafe Glockenspiel for breakfast twice.
It does not have air conditioning but except for one afternoon (arrival day in July) we did not need it. Nights with the large windows open were very comfortable. We were on the 5th floor - the elevator went up to 4, then we had 1 flight of stairs. Plenty of space.