If they don't plan to see anything between Vienna and Salzburg, they can fly into Salzburg. Otherwise they would just waste gas on an only mildly scenic motorway.

If they want to visit other places after Salzburg and need the car, why not take a taxi from Salzburg airport to the hotel (not really a distance to the Old Town from AP), and pick-up rental car once they leave Salzburg?

And they better drop it off in the country where they picked it up. Otherwise usually a steep surcharge for cross-border one-way rentals can apply. Check the fineprint.

Finally: If money is an issue they could check rates for rental cars from nearby Freilassing, Germany. Often it is much cheaper to rent in Germany than in Austria. Unless this would mean a drop-off in another country as mentioned before. Though the penalty charge for cross-border rentals between Germany and Austria or v.v. is often not as steep as elsewhere..

If they haven't decided about the actual flight and aren't going to do anything IN Vienna then they should look at the possibility of flying into Munich as well. Easy to take a train to Salzburg which takes only 1.5 hours. Lots of possibilities here.

At Salzburg airport there are several rental agencies in a garage connected by a walkway to the terminal. The Salzburg airport is quite compact and the reply to the original posting would be that it is better to fly to Salzburg and rent there, as the drive between Vienna and Salzburg is longer than you think and not particulary interesting. Check rental conditions about bringing the car to other countries, as from the airport in Salzburg you risk going over the border with Germany without even noticing.