Even if you are not religious, I think you should visit Troyan Monastery – it is a beautiful monastery hidden in the Balkan mountains. To be honest, I even prefer it over the famous Rila Monastery. In comparison to Rila Monastery, Troyan Monastery is smaller, but to me, it looks much more simple (and I think this is important when it comes to monasteries), yet still beautiful, and also quite cozy. Just like most other monasteries in Bulgaria, you can actually spend the night there. Of course, don’t expect modern facilities, but make sure you book a room in advance – here you will find contact details. Two places I found really nice are the monastery museum (which includes paintings and other items) as well as a small room where the famous Bulgarian revolutionary Vasil Levski used to hide. The room leads directly to the rooftop of the monastery so that he could escape in case members of the Ottoman empire checked the monastery without a warning.
The best way to reach the monastery is to travel by car – there are many interesting places nearby, so it will be much easier for you if you don’t think about bus or train schedules. It is located next to Cherni Osam river and there is a parking lot in front of it (in exchange to a small fee you can leave the car there while you explore the monastery). Of course, there are buses that travel to the town of Troyan, but keep in mind that the monastery is located around 10 km away from it. You can of course ask your local host to take you there (and just pay them something for the taxi services).
Close to the monastery you can visit the Natural Science Museum in Cherni Osam village, the National Exhibition of Popular and Artistic Craft in Oreshak village (me and my friends actually spent the night in Oreshak – if you also go there, I definitely recommend having dinner at Kaiser tavern) as well as the museums in the town of Troyan.