How can I find a suitable-level Chinese class in Beijing?
To answer my own question, I'm currently taking the part-time 1-on-1 classes from the LTL Mandarin School: https://ltl-beijing.com/chinese-tutor-beijing/.

I was attracted to this because (a) I Googled it and most reviews were good, (b) the prices are clearly listed, and it's exactly what I paid (so no "tricks"---what it says is exactly what I paid), (c) the teacher comes to my office, which is incredibly convenient, and (d) I could start immediately (no waiting for semester dates, no enrollment process).

I've had maybe 7 lessons thus far (2 hours each).  My comments:


I'm relieved that I'm not the top student; my teacher has students with better Chinese than me.  She knows how to help me.
I currently write a diary in Chinese, which I feel is a good approach as I want to learn how to discuss topics related to me.  These are not always comfortable topics.  E.g. my last diary entry was about my recent visit to Iran, and the impact Trump's sanctions are having there.  It's something I would talk about normally.
My teacher seems to understand how I feel about Chinese textbooks: they are incredibly boring, with fake dialogues.  I want opinions and controversy, not "Mike picked up Li Wei from the airport"---I want something I would be interested in reading ordinarily.  That being said, I still need to understand Chinese grammar, where it might be unavoidably dry.
My teacher is friendly and nice.  The two hours seem to go very quickly!