You should use außerhalb (outside of) together with "des Zimmers" (Genitiv). So the sentences become:
- Du musst Wasser außerhalb des Zimmers trinken.
- Du musst außerhalb des Zimmers Wasser trinken.
Grammatically both sentences are correct. However the order determines the meaning. In the first sentence, the meaning is: If you want to drink water you have to do it outside the room. (This is probably the meaning you want.) In the second sentence, it sounds to me more like: Whether you want it or not, you have to go outside and drink water there.
The construction with außerhalb des Zimmers sounds slightly non-native to me. Probably a German would rather say something like:
Sie können/dürfen hier nicht trinken.
Sie müssen draußen trinken.