As Laura said, you're talking about slow-travel country when you visit the Balkans and Greece. I figured on about 30 mph at best as I moved around via bus and (occasionally) train. The buses were comfortable, so there's no need to avoid them. It may work best to include 1 or 2 intra-European flights in your itinerary to avoid what might otherwise be 12- to 16-hour bus experiences.
As for places to visit, you need to do some reading and narrow down the territory you might want to cover. Be aware that unless you get up into the mountains, it's likely to be quite hot during the period you plan to visit.
Bucharest is far from the most interesting/attractive city in Romania. I would not go to that fascinating country and visit only Bucharest. I didn't cover the entire country, but I liked Timisoara (where the revolution began), Brasov, Sighisoara, Sibiu, and Cluj-Napoca. Costs are low enough in Romania that you might well find a 1- or 2-day tour in the NW (Maramures--wooden churches) or the NE (Bukovina--painted monasteries) to be affordable. Both are really interesting areas.
You skipped over Bulgaria, but I liked Veliko Trnovo, Plovdiv, and the two historic coastal towns of Sozopol and Nesebar. The capital city of Sofia might be a necessary way-station for the purposes of transportation, but it was not my favorite stop. Bulgaria is a great place to shop for inexpensive, attractive crafts.
If you go to Belgrade, Serbia (which does have its points of interest and sees fewer American tourists than many other large Balkan cities), I recommend a side-trip to Novi Sad, which has an interesting historic district. It's a good walk from the bus station, so check ahead of time on which city bus to take between the two.
The bus from Nis in southern Serbia (which I considered not too exciting) to Podgorica, Montenegro goes through some really lovely country. Podgorica itself is rather modern and is not where I'd want to spend much time. Kotor, Budva, Cetinje, Ulcinj, and Herceg-Novi are all more attractive, in my view. Since it sounds as if coastal Croatia is a must, you might visit Montenegro instead of Romania on this trip. It's easy to get to Montenegro from Dubrovnik by bus.
I would not go to Greece and visit only Athens. It's a hassle to get there (probably best to fly unless you want to visit Bulgaria or Albania), and there are so many interesting places to go both on the mainland and in the islands. My interest in classical ruins is pretty slight, but even so, I wouldn't want to go to Greece for less than 12 days, and more time would give you the freedom to consider visiting the large, interesting island of Crete.
I haven't been to Sarajevo recently, but if you go to Bosnia I'd also consider a visit to Mostar.