The best way to say it in Chinese is 什么时候走 (When do you leave).
“直到”, though literally means until, is a rarely used word in Chinese, and is usually considered the last choice to use when translating English. In many cases where you use until in English, you have to use other phrases in Chinese.
- This did not happen until 1998. → 1998 年以前没有发生过。(until here means before, so translation of before is used instead)
- Wait until two o'clock. → 等到两点再说。(until here means that you will do something else after two o'clock, so doing something else is used instead)
- Don't come in until I tell you to. → 我不叫你进来就别进来。(until here means that the former part (come in) will never happen if the condition in the latter part (I tell you to) is not met, so if-not-then is used instead)
And, for your case, the best translation is
- Until when do you stay here? → 什么时候走？
which is totally different than its English counterpart.
Therefore, my opinion is, whenever you want to translate something with until from English to Chinese, always try to use some other expressions without until.
You can also say 你在这儿待到哪天 or 你在这儿待到什么时候, which are closer to your original sentence. They are totally fine, but might take the listener a bit longer to respond.