National Art Gallery [wikipedia]
There are a handful of twentieth century Bulgarian superstar painters; unfortunately their English names are rarely Google-able and the museum has a strict ban on photography, which I think is a poor decision as some photos could spread the word about these obscure masterpieces.
Ivan Boyadjev - "Street in Karisruhe" (1923), "The Lent", "Townscape from Nuremberg"
Vladimir Dimitrov - The Master is his given title in Bulgarian art. He has some presence on the web, but his masterpieces remain safely unphotographed in the National Gallery.
Stephan Ivanov - "Nocturne" (1921)
Umberto Chiodi - Drawing and painting in the romantic style of Christian religious art combined with the playfulness of children's books on an intimate scale, his psycho-grotesque visions are captivating.
Dimitar Arnaudov - The National Gallery's special exhibition hall was dedicated to this painter's retrospective. I found his work to be bold and captivating. Of course, his best work is locked in the no-photo closet.

Sofia Art Gallery
In downtown Sofia this simple one level gallery is currently showing Bulgarian painters' self-portraits. The variety and quality of the images was astounding. Two really blew me away.
Krassimir Tsanov - Self Portrait (2006)
Ivan Obretenov - Self Portrait (2006)
My final plea: Museums! Allow non-flash photography or die of irrelevance!
360 Degrees Bulgaria
Sofia Street Art
The city streets are covered in graffiti. Much of it dwells in tags, the human equivalent of piss-marking your territory, but a few well done drawings light up the concrete.