The problem with renting a car in Vienna and dropping it off in Prague is the drop-off charges. They might be reasonable, but often they are many, many, many hundreds of dollars. If you were willing to do that for just the day in CK, then the CK Shuttle has early departures out of Vienna and late departures out of CK.
Everyone has different interests and a different style and pace they enjoy so what you have is probably perfect for you.
15-19 Oct: Budapest land at 0845. Assuming you are staying in a location well suited for a short stay, the taxi from the airport should only take about 40 minutes at most. Or you can do the 100E Bus (if you are staying in a well centered location) which is almost as fast. But first since you are under 65 pick up a 15-Day Budapest Travel Pass at the BKK office in the airport arrivals hall. It will cost you 5.650 ft (about $18). It will be the cheapest option for you. You could also use the BudapestGO App and download one. I just prefer the paper ticket. https://bkk.hu/en/tickets-and-passes/prices/15-day-budapest-pass/
The only special events going on are:
16-19 Art Market / Fair https://amb.hu/hu/: This is a pretty big deal if you are into the art world, but maybe a bit hard to justify with as little time as you have in Budapest.
At the Opus Jazz Club there is something every evening you are in town. I especially like Ephemeris and Petra Várallyay, the hometown girl and Liszt graduate done well.
You will want to do the Jewish section of the city on the 16th as some related stops can close early on Friday and not be open on Saturday.
As I mentioned before, get your train tickets from MAV. I just checked for the 19th of October and MAV 2nd class prices start at 13 euro plus 2 euro for the seat reservation while OBB 2nd class tickets start at 38 euro plus 3 euro for the seat reservation. Same train, same seats. Download the MAV app to make presenting the ticket easier to the conductor. https://jegy.mav.hu/ Oh, and I mentioned I would do first class. So those tickets start at 27 euro on MAV and 52 euro on OBB (plus seat reservations).
Finally i put some Budapest resource links on my profile page (click on my name).