Just use a timetable, e.g. https://fahrplan.oebb.at/webapp/#!P|TP!H|310398 and type in your route and date and you'll get possible connections (possible up to june 8th for most trains in Italy).

But you do know that Wien, Paris and München are about 8 to 12 hours away each? You'd need two days just to get there and back (for Wien and München there is a direct night train connection, too (except in summer)). 

Just Venice is a possible day trip.

Hektor, thanks for the reply. 

It took a few minutes, but I figured out how to switch the oebb website to English.  We are both retired and this is our first trip to Europe. We have family who are renting a house in Florence for all of October. We are planning two weeks in Europe and are trying to decide if we want to travel to and from Florence or spend a week there and fly to another destination for the second week. We’re looking for advice on what to do.  People we know have suggested flying to London he second week as opposed to taking trains from Florence. If there is another destination anyone would suggest that is close to a lot of interesting sites we would be very happy to know about it.   Austria and Germany sound interesting. London can always be another trip.   Any suggestions are welcome.

One thing, my wife is a dressage rider and would like to visit Vienna. Hopefully to see a show.

If you'd like to see Wien, than by any means do it. It's a beautiful City and the journey (even if it's a long one) is an interesting one, too on most parts because of the beautiful scenery you won't see when flying. 

One idea for this may be to do Venezia not just as a day trip from Firenze but to stay there on your way to Wien. Firenze has direct trains to Venezia and Venezia has direct trains to Wien.

Another possible idea: Leave Firenze in the morning, visit Venezia for a day (there is a staffed luggage deposit at the station) and take the night train with sleepers to Wien in the evening (must be booked well in advance).

From Wien, you may visit (as a day trip) nearby capitals Budapest or Bratislava or go to Salzburg.