As mentioned, this is a huge area, so I hardly know where to start. This is sort of stream-of-consciousness.
Podgorica, Montenegro's capital, is not a terribly attractive place, so I can't recommended it for a stay of any length. Places I liked in the country include: Ulcinj (in the south, striking Turkish vibe), Budva (intensely touristy), Kotor (the bay is a must; tourist load depends a great deal on whether a mega-ship is in port), Cetinje (interior town, a former capital), and Herceg-Novi (on the way to Dubrovnik). Without checking, I'd say Kotor might be the best transportation base among those options, but that may not be so critical for you since you'll have your own wheels. People say the national parks are lovely. Certainly much of the countryside is. The ride into Podgorica from Nis in southern Serbia was quite something. Hope you like curves.
I haven't seen much of Serbia. Nis is interesting enough but for me not worth a special trip (but that bus ride!). It was my way-station on the very long leg from Sofia, Bulgaria, to Montenegro. Beograd (Belgrade) is worth a couple of days, and you can make a side-trip to Novi Sad, the old capital, which is very distinctive. Or stay in NS and visit Beograd. NS feels a bit like a hippy enclave. Serbia is less westernized than some of your other countries; English is not as widely spoken there (not sure about things like museum labels, either), though I'm sure you'll find plenty of assistance if you need it. It's useful to know that menus virtually always list several sauces that you can get on the side for no more than about $1 in a typical restaurant. Take advantage of opportunities to try them. I liked the sweet-red-pepper version, which I think is called something like "ajvar". I once encountered it mixed into some sort of soft white cheese to make a spread: delightful.
[Edited to delete unneeded suggestions for Bulgaria.]
II spent more time in the larger Romania. The Communist ruler Ceausescu amused himself by having a great deal of historic architecture pulled down and replaced by ugly piles. You need a guide book to figure out which places best survived his onslaught (Bucharest not being one of them, though if you spend a day wandering around the city you'll see some scattered nice buildings, some early 20th century).
I give top marks to the folkloric area of Maramures in the NW with its gorgeous wooden churches, carved gate posts, Merry Cemetery, etc. You occasionally still see people wearing folk garb to church on Sundays. I took a 2-day tour that stayed in a B&B out in the country (don't have the name) and can't recommend a specific base to you. The former political prison in Sighetu Marmaţiei is very interesting if you get that far north. I saw nothing of the city itself.
In the NE (Bucovina) you have the also-beautiful painted monasteries. If I had to choose, I'd take Maramures because of the variety of sights there. Suceava is more or less the jumping-off point for that area. It didn't seem particularly attractive to me.
Cities with a lot of lovely old architecture (restored with EU funding, I believe) include the colorful Cluj-Napoca (closest to Maramures), Brasov, Sibiu and Timisoara (where the revolution started; good low-tech museum). Sighisoara, the most intensely touristy, looks medieval.
The western city of Oradea has some interesting Secessionist architecture. Not very touristy, but perhaps a bit out of the way.
Iasi is pleasant but not thrilling (though I missed the botanical garden). Skip it.
The Retro Hostel in Cluj-Napoca runs a lot of tours. The information on its website may give you some good ideas.