We have one day to travel to Salzburg from Vienna. We're looking for a reasonably priced day tour.
That's a very long day trip.
Take the train there and maybe buy a tour there.
That will make for a pretty long day as the shortest time on the train is two and a half hours each way from Vienna to Salzburg, plus your travel time from hotel to train station.
But if that is something you do want to do, then a cheap option would be to head straight to the old town area where you have the Castle on the hill, Morzart's house, several lovely old churches and other sites. Then only a short walk is Mirabell Palace on the other side of the river, and on the way to here you can stop off at Hotel Sacher for a delicious Sacher torte...
The first train to Salzburg leaves at 5:30am, the last train back to Vienna at 8pm. That would give you 12 hours in Salzburg.
Not so long for a day day trip...
There are several options for day trips. You can begin your tour in Vienna and transportation to/from Salzburg is included or you can make your way to Salzburg on your own via train and meet your tour group/guide there.
Salzburg is easily explored independently, there are bike tours, Sound of Music tours, and guided walking tours. There is also a HOHO bus.
I've done a day trip to Salzburg from Vienna, gave myself a few hours. But it wasn't my first time in Salzburg, then I stayed three nights.
Keep in mind if you're a Mozart fan, there are two Mozart houses in Salzburg, his "Wohnhaus" which you come across first coming from the train station and then the more crowded "Geburtshaus" after you crossed the small bridge.