Oh, yes, we do love our gold treasures. We have some of the oldest gold in the world - from the fifth millenium BC. It's in the National History Museum, I believe. And there's another one in Varna.
About what to add to the list: The National museum of military history - It has large exhibits covering the entire history of the Bulgarian army. They usually have special exhibits on May 6th. http://www.militarymuseum.bg/
There are some ruins near the mosque and the baths, right next to the mineral water springs. There are some at the lower level of the Halli, directly across from  the mosque. And hile you are there, you can sneak a peek through the fence to see some more roman ruins where the road used to be.
There's also the Roman Wall (at Roman Wall market, across the street from the Architecture University) whichi is actually Turkish.
Also near the Ivan Vazov theater and the City Park is Ivan Vazov's home. It's small but nice to see on the inside. That building - http://www.slovo.bg/vazovmuseum/P4020923.jpg
Oh, the St George church behind Sheraton Hotel - it's the oldest building in Sofia. Followed by St. Sofia church near the Alexander Nevski Cathedral.
And finally, if you are showing them NDK, be sure to show them the inside, because that's where the brilliance of the architect (whom my father knew:P) shines.

PS: Funny typo - "the crypt with ions". I imagined how we were building ion thrusters in the crypt of the Cathedral. That would've been awesome on so many levels. Thank you for the lovely image. :)