The Ivan Vazov National Theatre is definitely one of Bulgaria's most striking buildings. Originally built in 1906 by the Viennese architects Hermann Helmer and Ferdinand Fellner it has been extensively renovated several times. First following a fire in 1923, then again in 1945 after having been seriously damaged by British bombing during WWII and its last facelift was a 100,000 Euro project in 2006.
The building is as attractive inside as it is out but I don't know whether it is open for the public just to wander around or not. If you want a freebie (ish) peek inside then pop up to the loft restaurant Antique for a coffee and take the stairs back down and poke your head round a few corners - you'll be impressed!
There is a park in the middle of Sofia with a fountain (as seen here), and apparently it has different flower beds designed to represent different countries.
Anybody might walk through it, but a common sight is groups of old men sitting under trees playing chess. If you have the time to spare stop and watch a while.