"Sit on the chair where you like."? I think after "where", the sentence should be complete, but it's not, so only "which" is possible. Isn't it?
I'm assuming there are a number of identical chairs around a table.
"Sit on the chair where you like"
"Sit on the chair which you like"
Those two sentences might be understood in context but I don't think I've ever heard either of them said with the meaning we are discussing.
"Sit on the chair where you like" doesn't sound quite natural. It has a suggestion of "take that chair to wherever you like and sit on it" or even "sit on the part of the chair that you prefer". Better would be, "sit at the table where you like", "sit on whichever chair you like".
"Sit on the chair which you like" sounds natural, but again it has a slight ambiguity. It can suggest that you are choosing a particular chair rather than a position at the table. You want to say "sit anywhere around the table that you like", not "get the chair which you particularly like and sit on it" (that is a possible scenario but I don't think it's what you're asking about).
There are lots of phrases like "sit wherever you want", "take whichever seat you want", "take any seat you like", "take whichever chair you like", "sit at the table wherever you like", "sit at the table, anywhere's fine" etc .. so any that aren't quite right are easily avoided.
not a teacher