Sofia, Bulgaria

The tour has two evenings + 1 in day in Sofia, so I would say an awful lot. I've been there twice for only about 5 days combined but that doesnt make me a good source. Buy a good guide book. But I would go back in a heartbeat.

They mention quite a few things in the "Pre-Tour Planning" tab, if you're signed up for the tour.

"Here are suggestions for sightseeing in Sofia that we will not be doing as a group: National Art Gallery, National Museum of Military History, Sofia City Art Gallery, National Archaeological Museum, The Red Flat."

I've found quite a few other things that I'll be doing before and after my tour:
Banya Bashi Mosque
Church of Sveti Sedmochislenitsi (and lots of other churches)
Central Market Hall (mentioned as an "on your own" activity for Tour Day 2)
Sofia History Museum
Museum of Illusions
Ethnographic Museum
Borisova Gradina Park

Outside Sofia:
Boyana Church (a Unesco site, 1 hour from Sofia)
Vrana Palace and Park (2 hours from Sofia)
Dragalevtsi Monastery (2 hrs from Sofia)

I'm also finding lots of day trips, such as to Belogradchik Rocks in Bulgaria and others into neighboring countries.

Disclaimer: I haven't been on the tour (yet) so I'm not 100% certain that all of the above are not on the tour. I'm open to corrections, which will assist with my own planning.

Just an FYI - there seems to be a museum of Illusion in every city we’ve visited in the last year. They have just popped up all over. In my opinion they are a waste of time and money. They would be fun if you had curious children with you. We went to the one in Zadar. The one in Madrid was next to our hotel and always had a line of teenagers. My SIL actually got pretty nauseous from a few of the exhibitions. Anyway, if you have time to kill, go. Otherwise it is a definite miss.