I live in Tokyo - you can get a tiny studio apartment good for 1 person for $400/mo if you live 15-20 mins from one of the outer trains stations in a relatively old building, maybe like 45 mins-1 hr to get to the city center. You might spend like $50-$100/mo on utilities. Food is cheap if you cook a lot and use local ingredients. Eating out isn't cheap, but doesn't have to be expensive (a simple beef on rice bowl or some soba noodles for lunch might be $4, a bit more substantial meal might be like $6-$10, it and it'll probably be healthy).

How cheap you go really depends on your lifestyle - if you bike a lot instead of using the train, you'll save some money (aforementioned place to central tokyo might be $3-5 each way); if you eat out or drink a lot, you'll spend more money. But yeah, probably can do it if you're living frugally, for sure.

If it's $2k rent, you can definitely live on that without issues in Berlin, Tokyo, Beijing. I've lived in each of these places and you'll be fine. You may even be able to get by on $2k including food and transportation, depends on the exact type of housing you choose.

You mentioned a studio/1br, which you can totally do in Tokyo under $2k, including food and other daily expenses. However, it will largely depend on what you consider a decent social life.