Itinerary help

What city are you flying out of in USA?

You are facing the first step of planning a trip. You just need to sit down and figure it out using train schedules and flight schedules.

What I would do, but remember I value TIME more than I do CASH

I would pick the hardest place to reach within the trip to be the arrival city. That gets rid of one tough connection. In this case maybe Sarajevo or Belgrade or even possibly Dubrovnik. Then I would pick the furthest outlier for the last stop, in this case Vienna. Of course without checking all the connections I could be wrong. Its an interesting puzzle, but if its a 4 week trip you should be able to figure it out.

Another thing that might help is knowing that Budapest is a hub for Wizzair that provides cheap service to a few of your destinations. But the trouble is the connections aren't every day so you have to plan around then. Sarajevo to Budapest is under $100 but only on Friday. To find the cheap flights I use Google Flights. I put in the city I want to visit and then as destination I put in "Europe", and choose non-stop one way. Then I click through the days of the weeks and see what is available.

For some reason Czech Airlines does not show up on Google Flights. You will need to check them separately. They have excellent fares using Prague as a hub.

For trains http://fahrplan.oebb.at/bin/query.exe/en? is about as good as you can do.

Its your trip and I am certain you have reasons for the locations you have chosen, but you will get more bang for your buck and more time not traveling if you do the either the southern half or the northern half this time and the other half on another trip. Or maybe up the coast this time and the inland stops like Budapest and Prague next time.

Have fun

Zagreb and Ljubljana are quite close together. You can travel between them by bus or train. I don't remember which is faster, but I'm nearly certain the trip can be made in less than three hours.

There's one good train connection per day between Zagreb and Beograd. There is also a bus link. It's not a quick trip, but the bus was comfortable (as were all the many Balkan buses I took in 2015). The bus must have been quite a but cheaper or faster than the train, otherwise, I'd have made a different choice.

There's bus service from Zagreb to Dubrovnik; one or more connections will probably be required, and you'd be bypassing lots of nice destinations if you visit just those two cities in Croatia. I believe you can also take the train from Zagreb to Split and switch to a bus there.

Don't just look at trains; buses are sometimes faster when you're dealing with central European and Balkan destinations. Check fares carefully before buying a railpass; I think point-to-point ticjets will be cheaper for you.

I got a good one-stop connection from Zagreb to Washington-Dulles in 2015, but geograpically, Zagreb doesn't seem like a particularly good gateway for you.

Have you had the opportunity to consult guide books with comprehensive coverage of the area you're interested in? You're stringing together a bunch of capital cities (plus Dubrovnik), and I think you could do with some more variety--a Croatian island, the Austrian Alps, Plitvice Lakes National Park, etc.

I don't know how much time you have for this trip, but examination of the transportation challenges may show that you need to postpone one or more of your destinations until another trip.

I hope that this is a 3+ week trip to factor in all the travelling time between destinations.

The order of how to see these places depends on where you are travelling from and when. It would be better to fly open jaw to avoid backtracking. I would imagine that many of your destinations do not have direct connections to the USA.

Use rome2rio.com to start some route planning with your proposed travel dates. Although some places are relatively close together e.g. Dubrovnik and Zagreb, there is no rail service, so you would have to drive, take the bus or fly. Use skyscanner.com to check out airfares as this includes the value airlines such as Easyjet and Ryanair. Flights within Europe are best booked at least 6 months ahead for the best prices.

What do you want to see in each place? Why these cities?

I like puzzles.
Fly to Belgrade (underrated city. Love it. Also visit Novi Sad while there)
Belgrade to Sarajevo is something like a 6 or 7 hour trip on public transport. So fly Air Servia for about $100 nonstop in about an hour.
Find a tour company or a bus to do Sarajevo to Mostar to Dubrovnik.
Dubrovnik to Zagreb: you didn’t express an interest in the places inbetween so Croatia Air is under $100. Or make a several day trip of it and take the busses north.
Zagreb to Ljubljana by bus
Ljubljana back to Zagreb and then the train to Budapest (long train ride)
Budapest to Vienna by train.
Vienna to Cesky Krumlov by shuttle
Cesky Krumlov to Prague by Shuttle
Prague home.