My family and I will be driving from Taesch to Salzburg in July. We don't have much time to spend in Salzburg, and would like to get there if possible in a day, if not, we'll break it into 2. We will be coming from Zermatt, so would have seen some of the Swiss Alps. What route would you recommend that would allow us to experience and see the Austrian Alps without going too much out of the way? Or just any scenic/picturesque route? If we should stop overnight, where's a good place that will not cost too much? Thanks in advance for any help you can offer.
www.viamichelin.com will suggest 3 routes. all taking between 8 1/2 and 10 hours. Assuming you rented the car in Switzerland, it will come with a Swiss vignette toll sticker. So you will need to buy an Austrian vignette at the border. Be sure all drivers have International Drivers Permit.
Speaking of car rentals, have you considered the large fees if you drop the car in a country other than the one you rented in?
Do you want to drive because of a particular reason or because you are from a culture where driving is the customary default?
The reason I ask is that a likely more pleasant experience might be had on a train trip of a bit less time, or about the same maybe.
You could leave Täsch at 8:48 towards Visp on the little red Matterhorn Gotthard Bahn getting to Visp at 9:46. You'd have 11 minutes to go inside and get to the inside platform. That's plenty of time to go downstairs, over one platform and up again.
You can visualise it by the main photo on this link to the station webpage https://www.sbb.ch/de/bahnhof-services/bahnhoefe/bahnhof-visp.html?tracking-marketingurl=bahnhof-visp You will arrive probably on platform 3 which is in the middle of the photo, on the island. You should be able to see the "3" on the lamppost in the centre of the photo. You need to probably change to platform 4, towards the left of the photo - you can see the "4" behind the clock. All Swiss main platforms are broken into areas A, B, C, D which shows which part of the train you are standing in front of, so you are actually looking at 2A, 3A, and 4B. You can see that that would be an easy change. Scroll down and there is a link to a map, showing the tunnel between platforms.
The SBB Swiss train leaves at 9:57 (Direction: Romanshorn) to Zürich HB and arrives at 11:58 with a 42 minute connection which will give plenty of time for you to source a picnic to take on board, and it will be lunch time.
Leave Zürich HB at 12:40 on the Railjet going to Bratislava hl.st. and you will arrive at Salzburg Hbf at 18:03.
Everybody gets a great view, everybody can enjoy the picnic on board zipping through the countryside.
If you decide to drive, you will have a very expensive and long tunnel through the Austrian Alps which is not covered by the Vignette which you also will need, and in Austria every US/Canadian driver is required by law to have an in-date IDP in addition to the home driver license. Add about 25% to the times quoted to drive by Google Maps and Michelin. Those times will then need to be expanded by food and toilet stops.
Apart from money considerations - like extra auto hire fees, vignettes, tunnel fees - an important consideration is that the zone around Brig has very good railway connections through tunnels, not so for road connections, so a trip to/from Zermatt area may be really easier if done by train than by car.
I may have missed this in your post, but are you planning to drop the car in Salzburg? Renting from one country and dropping in another often comes with a hefty drop charge. One other point to mention is that parking in Salzburg can be expensive.
As others have mentioned, each driver listed on the rental form will require an IDP and don't forget about the Austrian Highway Tax Vignette. Those caught without one will face hefty fines, which are usually collected on the spot!