Hissar, or up in the rhadopes
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I've been living here for four years. If I had a free month to write I would definitely go to hissar, close to Plovdiv. On summer nights, with the fireflies in the ancient fortress it is magical, but still not too touristy. There are plenty of day trips and you can get up into stars planina or the rhadopi for a weekend. Also, the guy who owns the stables there is rather nice, if you ride.
Alternatively, shipka is gorgeous and has more hiking/biking opportunities, as well as an English family. Again, plenty to see but not overly touristy.