I should have planned this trip long ago but things kept getting in the way of any plans. My wife and I (both 77) want to fly from Texas to Switzerland/Austria in early October. We need to have a car in the vicinity of Zurich for some family genealogy research. Other than that, my wife would like to go to Vienna and Salzburg in addition Melk Abbey and Dornstein (sp?). We could fly to Zurich and rent a car and use it to drive to Salzburg, Vienna, etc. However, if we were returning the car to Zurich, we would cover the same territory, going to Vienna and returning to Zurich.
We would arrive via plane in Zurich and would not need to be back for a return flight to the US for about 21 days.

Maybe we should take a connecting flight to Vienna and rent a car there and eventually turn it in at the rental agency in Zurich. We would like the opportunity to stop at any interesting place along the route to Zurich. I need to study the map along the route and plan our tentative stops. B&Bs in the smaller places attract us. Your itinerary suggestions will be appreciated. I need to confirm airline reservations within the next 4 or 5 days.

I am no expert on exactly what you want to do, but the train system in Switzerland is outstanding, so I would try to use that whenever available instead of driving your own rental car around.

The absolute best way to get around in Switzerland (and Austria for that matter) is train and bus.

Where near Zurich will you be that you'd need a car? Trains/buses go just about everywhere and are a pleasure to use.

I suspect you'll find that rental rates are crazy expensive...as is parking.

Could you fly into Zurich and out of Vienna, or vice versa? (Before you say the fare would be too much, figure out the cost of backtracking to Zurich.)

Car rental rates are pretty crazy this year, and a one-way rental (esp. involving different countries) would be especially expensive.

Jean, I think your suggestion is great. I think we'll fly to Vienna, travel back through Austria to Switzerland via train, etc., avoid renting a car, and eventually fly back to Texas from Zurich. Thank you for your help.

I don't know how long the Swiss leg of your trip will be, but when I went in 2016, we got a 15 day travel pass that covered everything but high mountain lifts (and gave us a discount on those). The great thing with the pass is that, where we wanted to go, the SBB app would come up with an itinerary that, even when it involved transfer from trains to busses, or even boats, was easy to follow, and didn't require us to purchase tickets for each journey. It was the most liberating travel experience I've ever had in Europe.

"However, if we were returning the car to Zurich, we would cover the same territory, going to Vienna and returning to Zurich."
Of course not!
There are tons of different and extremely attractive itineraries between Vienna and Zurich.
If you need a car (I don't think so), you can rent it in the Austrian town of Bregenz, just 1 hr by train from Zurich airport, and drop it off in Vienna.
BTW: I cannot imagine a place in the Canton of Zurich that cannot be reached by public transport (usually every 15-30 minutes or so).

You could plan a circular route to visit one set of locations on the way to Vienna and another set on the way back. For example, you could pass by Lichtenstein and take a high Alp road (depending on the season) to Innsbruck and wend your way in the Alps (Hallstatt arriving in Vienna from the southwest and return by following the Danube to the German border to visit locations such as Melk Abbey, Wilhering, Steyr, etc. including Neuschwanstein in Bavaria. You could include Salzburg in the mix from either direction.

https://flic.kr/p/2jdazN9 https://flic.kr/p/7pERR6 https://flic.kr/p/7pJKKS
https://flic.kr/p/7pJMiW https://flic.kr/p/7pJR4N https://flic.kr/p/7pJRSo
https://flic.kr/p/7pEZTT https://flic.kr/p/7pEYKa https://flic.kr/p/2jdcxRq

A circular route is not backtracking. The OP could travel via Lichtenstein, Innsbruck, Hallstatt etc. driving in the Alpine area and return via the Danube valley through Germany to include Neuschwanstein. Different things to see in different scenery. But if the driver feels nervous about driving in a foreign country in general, it is best to minimize the use of a car.

Update. We are flying from the US to Vienna and returning to the US from Zurich three weeks later. In that time we'll spend 4 or 5 days in Vienna and the surrounding area. After that, we'll visit Salzburg & Munich in no particular order. After those, Switzerland will be next and that part of the trip is still a work in process. I'm going to see what is available in the AirBNB world.

If you haven't already booked your airfares, make sure to book a single multicity ticket rather than two one way tickets (it would normally be cheaper to do this). Of course, you probably already know that but not everyone does.

Dreamon, thanks for the advice!