How best to maximize our time in Europe

I'd focus on one city rather than trying to do boht. Vienna is a magnificent city with so much to see. Spending one night there is far too little. You'll arrive one day, see some things, sleep in Vienna, then travel out the next day. Frankly, I'd pick between Vienna or Prague rather than trying to do both. Prague is a beautiful city with a lot of history. Get the Rick Steves books on those two cities and see what speaks to you.

First, the nonstop from Georgia to Budapest is from Kutaisi not Tiblisi. From Tiblisi there are no nonstop to any of the three. So you have a 6 or 8 hour trip to Budapest. The 7th will pretty much be a waste. If you spend 2 nights in each city you will spend all your time traveling. Pick one and do some day trips or do two cities at most. Budapest and Vienna are 2:40 apart Prague and Vienna about 5 hours.

Or, i guess add a night to Budapest, skip Vienna since you have larger plans for Prague. Still a less than desirable deal. The 8am train arrives about 3:30pm or the 2:30 RyanAir flight arrives at about 3:30pm.

Or just fly Tiblisi to Prague and do the one.

Our flight from Tbilisi is not direct we go from Tbilisi to Istanbul to Budapest.
After Budapest, nothing is set in stone. I would like to have some sense of a plan to avoid spending too much time traveling and/or making decisions.
Your recommendations are appreciated as we zero in on a plan.

Turkish Air. And is your flight home from Prague already booked? If yes then think about half your time in Budapest, maybe Eger and Szentendre but all as daytrips ... then ... the other half in Prague with maybe Cesky Krumlov and or Karlstejn Castle or Kunta Hora.

Thats about all the town you have if you want to see any of Budapest and Prague.

Yes Turkish Air. The flight home has not been booked as of yet. We have agreed that a trip to Cesky Krumlov is a must do.
We haven't sat down and made a priority list for Budapest or Prague or Vienna so we can adjust to whatever makes the most sense. It's tough to eliminate things when you are so close. The desire to see as much as possible is hard to supress. I am beginning to come around to the idea that removing Vienna would create more time in Prague. Its such a challenge. Thank you all for your seasoned advice.

I must do things this way to get my head around them. But in this case I am no help. Sorry.

7: Budapest, 06:45 to 13:15 Turkish Air to Budapest (8.5 hours of travel). Means you are getting up at 3am. I usually think it’s best for a first-time visit to stay someplace along Andrassy ut, but with a 1.5 day visit I think staying closer to the river is a better idea. If you are on a budget look at the D8 https://d8hotel.hu/ with a bit more to spend look at the Intercontinental https://www.ihg.com/intercontinental/hotels/gb/en/budapest/budhb/hoteldetail

You are working on little sleep so I am not sure what you might be up to for tourism. You could do the river front on the trams, Great Market Hall to the Parliament. You could take the M1 to Heroes Square and then walk back to the hotel and see all the opulence and architecture. You could go to a bath house, get in the water and sleep. Some of the best of Budapest is the lights so if you slept a while then whent out, that works too. Dinner if the weather is good might be DunaCorso.

8: Budapest, There is so much and you have so little time any suggestions would be a stab in the dark. Maybe hire a guide and get a royal tour.

9: Morning train to Vienna

10: Look around Vienna

11: Morning shuttle to Cesky Krumlov

12: Morning train or shuttle to Prague

13: Look around Prague

14: Use the excellent train system to look around

15: Depart

Each to their own. If you were to drop Vienna and go straight to Cesky Krumlov (shuttle) then you would have two more days to put someplace. Maybe more trips on the excellent trains in the Czech Republic, maybe more time to see Prague and / or Budapest.

Your head is spinning because you’re trying to cram a 2-week vacation into 6 days. The specific advice you’ve gotten is, I think, good. Hopefully it shows how little actual sightseeing you’re getting from those 6 days.

So…I don’t know how much you’re spending overall on this trip, but if taking a $250 bath on a couple of Turkish Airlines flights makes your trip infinitely better, maybe use some of the above advice to create a more practical, pared down, itinerary?

Chris, yes, you nailed it. The OP already bought the Turkish Air ticket or I would have suggested a few days in Kutaisi which is a facinating city and suffering less from disturbance than is Tiblisi right now. My son wanted us to go to Georgia this summer but his boss, a guy named Pete, so no way Jose. Kutaisi has the non-stops to Budapest, cheap too.

Another option if the OP has any flexibility in that ticket is to lay over in Istanbul for a few days, then go to Budapest, then go home.

Chris that is spot on. When we originally made the decision to go to our friends wedding we mentioned the places we could go in the days after. (Budapest, Vienna, Prague, etc) Now as we begin planning, and from the discussion on this forum, its becoming obvious that we need to trim the itinerary and focus on seeing more of a couple of places instead of very little of too many.
The option to go to Kutaisi was discussed, but the airline, Wizz Air, doesn't list any flights for the days we will be there. Nor are there any flights to Prague from Kutaisi. Disappointing because I had read the train ride from Tbilisi to Kutsaisi is a nice trip.
I am not that interested in a Turkish bath.
So, that being said. if you had to eliminate one of the three options, Budapest, Vienna or Prague which one would get the ax?

If Budapest requires more time then it makes sense to me to remove it from the itinerary and spend more time in VIenna and Prague.
This discussion is very helpful. I also have adopted the suggestion and have begun writing down times/places to get a visual of how much time is available and being used. Thanks again.

I would recommend 2 cities, Budapest and Vienna and fly out of Vienna. Prague is nice, but IMO Vienna is a greater city and has much more to see.

Threadwear, unless the OP is 28, single, and traveling with his buds. In that case he should just go to Prague.

Single. Travelling with female friend and way past 28.😁

Budapest its sexier and more lady class. https://youtube.com/shorts/IQTqpsKFjR4?si=WmVZtslg-88LLT6z

Vienna for those that dream of the return of empires and want to see the legacy in museums.

Prague for rare surviving medeavil architecture and heavy drinking.

I would go to Budapest and Vienna. Been to Prague and Vienna. Confess to desire to see Budapest. Loved Vienna way more than Prague.

You have 8 nights after the wedding. Give four nights to Budapest and four nights to Vienna. Three hours by train between the two? Only a half day lost to travel. (Budapest 6/7 to 6/11. Vienna 6/11-6/15.)