For starters I get the impression you like sweets so I suggest you check out Lime. It's a fairly new place on Graf Ignatiev street number 40 opposite the street market and the church. It's a small place, where smoking is prohibited. The prices are more than reasonable. I tried the yoguhrt and lime cake which was divine and a big piece was only 3.30 leva! The tea was incredible and with a fun twist at least for me(I won't spoil the surprise), and they have more cakes, sandwiches and drinks to try. And the take-away is 15% cheaper than consumption on site which is something common in Greece for example, but not a practice in Bulgaria. 
I recommend the place. :) I'll be glad to hear your reviews about it. :)