If hiking interests you, I'd recommend the Rhodope mountains in Bulgaria -- there are a lot of popular tourist trails between the mountain refuges.
The mountain is virtually uninhabited (there are a few large-ish towns and small villages), so if you are tired of civilization, this might be something to consider.
Depending on your interests, you can choose between historical sites (such as Perperikon , which I highly recommend), natural wonders ( Trigrad Gorge , Marvelous Bridges , etc.), spa centers/mineral water resorts (for example, Velingrad and its surrounds), ski resorts (e.g. Pamporovo ), caves ( Devil's throat ) or Christian monasteries ( Bachkovo Monastery) .
Following most of the trails could take between 2-3 days up to a week or more, depending on your time constraints, and you'd probably still miss some places of interest.
The best time to travel is from late spring to mid-summer, when the temperatures will be high enough to travel without too much equipment.
Drop a note
if you need some further pointers, I'd be happy to help.
Disclaimer:
Being Bulgarian
, I'm obviously biased, so take this with a grain of salt.
travel.stackexchange.com/users/793/mindcorrosive
In Montenegro: UNESCO-protected Kotor Old Town, Ostrog Monastery, Cetinje (Historical Capital), Skadar Lake.
If you have enough time, it would be nice to see some mountains too: Zabljak, Durmitor, as well as Biogradska gora.
If you'd like to take part in night life than Budva is very good and while you're there, you could visit Budva Old Town.
Also Maximus is located in Kotor and it is the biggest night club in Montenegro.
travel.stackexchange.com/users/1305/Nemanja Vujacic
Well I can recommend the Transylvanian mountains in Romania.
Bucharest you'll likely go through (the capital)
but I found it a bit dull and oppressive.
Head out to Brasov in the mountains, a fantastic town, and with lots to do in the mountains all around, from Bran Castle (marketed as Dracula's castle), a mountain fortress and more.
And if you're lucky, you'll see some bears as well!
travel.stackexchange.com/users/101/Mark Mayo
In Bosnia, must sees are Sarajevo (2/3 days should be enough), and Mostar (1 day).
travel.stackexchange.com/users/506/Thomas Radioyes
In Bosnia, besides Sarajevo and Mostar, there is Pocitelj, Kravice waterall, Hutovo Blato, even Stolac (all Herzegovina is very lovely).
travel.stackexchange.com/users/1953/mem
I'm already planning my next vacation in next May or late August/early September. I'm planning to visit the Southeastern part of Europe. Im especially interested in Bosnia and Herzegovina, Montenegro, Albania, Macedonia, Bulgaria, Romania and Serbia. The time limit is 4 to 6 weeks. I´m interested in tips that are worth a visit, especially cities and natural sights, so that I can plan a great tour.
Roadtrip in Southeastern Europe
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<europe><road-trips><eastern-europe><balkans><southeast-europe>
travel.stackexchange.com/questions/1817
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The best time to travel is from late spring to mid-summer, when the temperatures will be high enough to travel without too much equipment. The Rhodope mountains in Bulgaria are good for hiking, or you could visit Bran Castle (marketed as Dracula's castle) in the Transylvanian mountains in Romania. Zabljak, Durmitor, as well as Biogradska gora are also worth seeing. In Bosnia, besides Sarajevo and Mostar, there is Pocitelj, Kravice waterall, Hutovo Blato, even Stolac (all  Herzegovina is very lovely).  In Montenegro you can visit UNESCO-protected Kotor Old Town, Ostrog Monastery, Cetinje (Historical Capital) and Skadar Lake, as well as Maximus in Kotor, which is the biggest night club in Montenegro. South East Europe is full of interesting places to visit. Bulgaria offers mountain hiking, as does Romania along with a chance to visit Dracula's castle. Montenegro offers historic towns, mountains and amazing nightlife. Finally Bosnia offers the must-see city of Sarajevo, among others.
The Rhodope mountains are good for hiking in Bulgaria. Best time to visit is spring-summer. Montenegro has many sites worth visitng including historic towns, lakes, mountains and nightlife. Romania has the Transylvanian mountains and Bran castle, famous as Dracula's castle. Sarajevo is a must-see in Bosnia, as well as many other places of interest including Mostar.