For us, we are in Bulgaria because of our children. (Bulgarian husband, I am American). We live in a smaller town, so some of the things that apply to us may not apply to larger cities. For example- it was really easy for us to enroll our kiddo in daycare and then kindergarten, but in Sofia or Varna the waiting lists can be very long.
We started my son in daycare at 18 months, mainly because we wanted more exposure to the Bulgarian language and also because I was ready to go back to work. I was concerned at first, because I have heard horror stories about how "terrible" the Bulgarian daycare system is. But I will say my son loved his teachers and they were attentive and affectionate towards him. Of course, we had our favorites, but none were incompetent or bad teachers. He learned potty training at daycare in one week around two years old. It was awesome! He also became much more independent about feeding himself, singing songs in Bulgarian, playing games etc.
He just moved up to kindergarten (3.5 years old. Kindergarten is from 3-6, with the last two years mandatory) and he really really likes it. They are implementing a new system (not sure if it is nationwide or in our city) and the kids all get personalized portfolios to track their progress through kindergarten. My son comes home every day and shows me the songs he sings or the dance he learned. And the teachers chat with me about the best way to get him to sleep (my son is a difficult sleeper) or his eating habits and how to raise a happy kid. They seem really warm and caring. One of the kindergartens in our town is switching to Montessori method, but it is still a public school- so the fee is still around 40 lev a month. (Versus private kindergartens that are usually around 400-600 lev a month)
Starting in the second year of kindergarten, the kids can take up to two electives a week which usually include basketball, soccer, singing, ballet, yoga, traditional dance, karate etc. These require a small fee, usually around 3 lev a class.
The teachers all seem amused that my son is a foreigner, and some speak English. He had the cutest relationship with one of his teachers where every day he would teach her some English and she would teach him Bulgarian. But my son's Bulgarian is almost as good as his English now.
Playdates tend to be a "call on my way over to make sure you're free" kind of thing, at least for me. But I don't have a lot of play dates for my son. I'm shy. Plus, I like scheduling things in advance and not a lot of Bulgarians I know are like that. Once kids are around 5-6 it is more of shout over the fence to see if your kiddos are home
After school activities- in our town there are a ton of private lessons. Everything from musical instruments to sports, swimming, dance, robot club, scouts etc. We are not enrolled in any yet as they usually start from age 4 or 5.
All in all, I am very happy with the life my kids have here. Are they missing out on some opportunities they might have in the US? Yes. Are they getting other opportunities here? Yes.