You will find any number of good places to eat - it might be easier to list the places to avoid!
As for local dishes, try these -
Shopska salad - mixed salad covered in shaved feta-style cheese, ususally offered as a starter
Kvarma - a (usually) thick stew with meat & onions, served in a bowl
Kebapche - a spicy cross between a sausage & a burger
Kebapcheta - smaller version of above, more like large (flat) meatballs, you will normally be asked how many you want
These are just a few, there are loads more, and I'm sure you will get a lot of answers with personal favourites