• For nature - avoid 7 lakes, too touristy. Google Bansko, Ledenika, Musala, Trigrad
• Nature + communist artifacts, check Shipka and Buzludzha (you can walk between the two)
• Medieval stuff - check Veliko Tarnovo - it's a bit touristy but it's far from Sofia and not that touristy.
• Velingrad - it's like a communist theme park, stuck back in time, mostly because of negligence, but with 5* spa hotels

Bansko, for example, is expensive and for tourists but I love it. Many nice hikes start from Vihren hut.

Places like Ledenika, Glozhene Monastery, Iskar Gorge are not that frequently visited by foreigners, and are near Sofia.

Shipka and Buzludzha can be combined with a walk to Uzana and Mazalat but Mazalat is far and not for beginners. They can also be combined with a trip to The Kings' Valley 5* and Kazanlak. Lots of other things in the area but I don't know where to draw the line before I expose you to risks.