Eastern Southeastern Europe for 2-3 weeks

Romania is huge - you could easily spend 10 full days there, and then some (not just Transylvania, but Maramures and Bucovina regions up north and Timisoara, Oradea, Cluj-Napoca to the west and northwest). If you have extra time, why not spend the rest of the time just in Hungary or in Bulgaria and fly back from Budapest or Sofia? Trying to weave your way all the way to Berlin sounds like a lot of wasted time in transit. None of the cities you mentioned (Berlin, Vienna, Prague, etc) are in southeastern Europe. You're trying to do too much IMHO...Kiev is even more out of the way. If it were me, I'd stick to a tighter geographic area consisting of Romania/Bulgaria or Romania/Hungary (or Serbia).

I agree that I should keep it to a few countries. How easy is it to fly from Kiev to Bucharest? I only want to spend a short time in Ukraine (visiting Chernobyl mainly) and maybe. Few days in Kiev. I've heard there is a train from Kiev to Bucharest but it takes 24 hours at least. Are there domestic flights into Romania? Any ideas which would be the cheapest cities to fly into from NYC? Thinking mid/September

How easy is it to fly from Kiev to Bucharest?

For all flight questions, just type them into google and you'll get an answer:
e.g. "kiev to bucharest flights"

Cheapest flights from NYC to Bucharest would probably be through Turkish Air (they're the cheapest for just about anything). For April, I found < $600 round trip but ~ $800 is typical.

Here are some Romanian itineraries - I think they assume you are driving, although you can use trains as well. Transylvania itself is a big region.
http://romaniatourism.com/sample-itineraries.html

Here's my suggestion, focusing on Romania highlights then Budapest:

Bucuresti - 2-3 Nights (Palatul Parlamentului, Village Museum (Parcul Herastrau), Old Town; meal at Carul cu Bere)

Brasov - 2-3 Nights (Sinaia and Peles en route [closed Monday]; stay at Hotel Kolping in Poarta Schei neighborhood; Mt. Tampa; meal on Strada Republicii/Piata Sfatului; day trip to Rasnov Fortress and Bran Castle)

Sighisoara - 2 Nights (Clock Tower; Church on the Hill; meal at Casa Vlad Dracul)

Sibiu - 2 nights (Piata Mare, Council Tower, Bridge of Lies)

Deva/Hunedoara - 2 nights (en route, visit Alba Iulia and its fortress, bulwarks, and gate; old Capital and churches; Corvin Castle!)

Budapest - 5-7 nights (Fisherman's Bastion; Matthias Church; Citadella; Rudas baths; Parliament; Great Synagogue; Opera House; Szechenyi baths; Heroes Square;....)

Add flight to/from Kyiv or finish in Vienna - 3 nights

Or flip it and start in Vienna or Budapest and finish in Bucuresti.

You should definitely visit Kiev, it's amazing place. Then you could travel to Carpathian mountains and then to Romania. I think, it will be the best route for eastern Europe. We are in Ukraine now, but we are using tour operator http://touristclub.kiev.ua/ . That's why our tourist routes already determined. I've never been in Romania but i definitely recommend you to visit western Ukraine, especially Lviv.

IF you visit Bulgaria and IF you want to rent a car, be prepared for MAJOR potholes on the roads. We rented from Drenikov in Sofia, as they were much cheaper than other options we researched. It was basically a rent-a-wreck, an old VW station wagon with bad tires, oft-patched inner tubes, and a loose underbody panel. It may cost more to have a reliable, late-model rental car.

For long train trips in the Balkans, double check that the train is currently actually running. I ran into a small tour group on the train from Bucharest to Veliko Trnovo (Bulgaria). They had already had one overnight train ride turn into a bus trip and there was another coming up.

I took a lot of buses in Romania and Bulgaria. The buses themselves were comfortable (air conditioned; no on-board toilets, but they stopped about every 2 to 2-1/2 hours), but there are some bumpy roads. Both trains and buses are quite slow.

Romania is a fascinating country. I hit most of the places mentioned by others and would happily return. The art deco architecture in Oradea, near Hungary, is also nice. Timisoara, also in the west, is both pretty and historically important; the revolution began there. This seems the most cosmopolitan city in the country after Bucharest.

We are planning a trip to Romania this April. I have found the Rome2Rio site very useful for figuring out the best places and ways to transfer between cities and countries. For example, looks like there are several trains a day between Budapest and Timisoara, Romania for not too much (17-24 dollars) and only 4-5 hours. As far as travel in Romania, we are doing a 1-way car rental with Sixt from Bucharest to Timisoara. The 1-way fee is an exta $130, but we realized we can go to more out of the way places and travel at our speed (and not have to wait for infrequent trains between many places). I also use the Matrix site to look for the cheapest flights. We decided not to go to Ukraine, but will be going to Belarus from Budapest. The visa process was not easy, but we are excited to see Belarus. Happy travels!

We are planning a trip to Romania this April. I have found the Rome2Rio site very useful for figuring out the best places and ways to transfer between cities and countries. For example, looks like there are several trains a day between Budapest and Timisoara, Romania for not too much (17-24 dollars) and only 4-5 hours. As far as travel in Romania, we are doing a 1-way car rental with Sixt from Bucharest to Timisoara. The 1-way fee is an exta $130, but we realized we can go to more out of the way places and travel at our speed (and not have to wait for infrequent trains between many places). I also use the Matrix site to look for the cheapest flights. We decided not to go to Ukraine, but will be going to Belarus from Budapest. The visa process was not easy, but we are excited to see Belarus. Happy travels!

Chris C, you are choosing well. I have been to every place you list (most on several occasions) with the exception of Bratislava (Slovakia, yes; Bratislava, no). I love the region; especially Hungary.

We are off to Kyiv in a few months (Kyiv + Budapest of course). You should watch this on Netflix: https://www.youtube.com/watch?v=RibAQHeDia8 Its powerful.

So I've updated my itinerary. 3 weeks total flying NYC to Kyiv. I will be spending 4 days total in Kyiv with a day to visit Chernobyl. Will then take the train to Lviv and spend 3 days there. From Lviv I will be taking a train to Solotvyno then crossing the border into Romania at Sighiu Marmatei. From there I will spend a week in Transylvania. This leaves me one more week to get to Budapest. I'm not super interested in spending many days in Hungary. I'm considering maybe a few days in Belgrade? My flight back to the US is from Budapest. Suggestions on an itinerary for the remainder of the trip?

Where do you plan to end your Transylvanian odyssey?

Getting from central Romania to Belgrade can be a time-consuming process by bus or train. I think the route would go through Timisoara, which I found very attractive, and it has about the same travel time to Budapest as Belgrade does.

Belgrade is interesting, but many people say Budapest is one of their favorite cities. I doubt that many would say that about Belgrade. If you haven't already seen Budapest, I'd consider spending time there rather than in Belgrade.

Novi Sad makes a nice day-trip from Belgrade.

I am going to assume you checked out the time and cost on Wizz and the Ukraine airlines and Tarom in lieu of those long train rides.

There are no domestic flights from Ukraine to Romania from any city in either