My husband and I are taking our twin 18 year old granddaughters to Salzburg. Arrive on July 21st and leave on July 24th. Would like an apartment with 2 bedrooms. We will have a car. Want to stay fairly near to the Old town. Looking for something between 200 and 400 dollars a night. A/C would be nice and a small kitchen.
Using booking.com and selecting 2 bedrooms, kitchen, parking and a/c in the under $400 range produced 3 results for your dates.
Did not research how close to "Old town' they are.
Without a/c added 5 additional results.
A similar search on Airbnb showed a lot of results which can be winnowed down by adding features like A/C and restricting to a certain city area by zooming into the shown map.
Having a car and staying close to the old town isn't really the best combination.
If you have a car, staying in the Old Town will have parking challenges as much of it is pedestrian only. You’ll probably end up paying a lot to park in a public lot.
If you have a car because you will spend most of your time exploring the stunning surrounding area, consider staying outside of the city center. Then you can take the bus into the city, or park in the large parking lot built into the hill (where the fortress is).