Is there any daycare that offers daily drop-in classes for a preschooler in at least 50% English language? Where I could drop my kid off for say 2-4 hours at a time? And pay for individual sessions, or for a month of drop-in sessions?

Preferably near 1) 关上 guanshang district; 2) 大水田 DaShuiTian / 大冲村 DaChongCun; 3) jinbi residential district

I doubt you will find such a thing here .What you are looking for matches more of a baby-sitting situation where the baby-sitter is bilingual and can teach the child English with games, etc.

There are many pre-school places around time. Some of them are posting ads here looking for a teacher. If I were in your shoes, I would walk around the neighborhood and search and ask the neighbors with kids. I'm sure they can give you first hand accounts what is available.

Yeah I'm looking for something like Gymboree classes, where kids can have open play time, or can have teacher-led 1,2,3 hour sessions in either art, music, math, learning, etc.