Hey mathijs123,
I am from Bulgaria and I am really glad that you chose Bulgaria as a destination. I live in Sofia, but I would recommend you to visit mostly the landmarks near the smaller towns. There are some really beautiful places to see. For example, the Tsarevets castle and Arbanasi near Veliko Tarnovo (which is not exactly a very small town, but coldwarspy mentioned it and he's right :D ) or villages like Ribaritsa (also a must see), Karlukovo (where is the Prohodna Cave), Melnik (very nice place with great wine
), and many more. There are many such places, it would be better if you take some kind of traveler's guide with you.
Well, from the bigger cities you could visit Sofia, Varna, Burgas and Plovdiv (and more precisely the old city of Plovdiv, there are the old style houses)....
For traveling I would recommend you the bus, cause trains may be a very bad experience here sometimes. You should be also very careful with buses, cause they are usually not so comfortable. The bus company that I usually use are BIOMET.
Also taxis are not a good solution cause they usually charge foreigners way above normal. Just avoid them whenever possible.
The best option sometimes would be to rent a car (if you have the opportunity) cause sometimes there is no transport to the smaller villages where the attractions are, and most of the time it is much more comfortable.
Well that's all I can think of at the moment. If you need any further info or if you want to know particular prices, places, things, etc., I'll be glad to help.
Best regards