Yes, that's right, Kyle. To be a purist you could say "Where do I have to put that" or "Where must I put that" seeing that it's "dois" rather than "devrais". I think Chrispy is trying to translate mettre/poser as the phrasal verb "put on", whereas "put" on its own is fine. If you wanted to keep it as a phrasal verb you could say: What do I have to put that on? Chrispy - is my attempted translation of this last sentence OK? --- Sur quoi dois-je le poser/mettre?

I agree with the other members. The natural way to translate 'Où dois-je le mettre' is 'Where should I put it?' You don't need the 'on'. The verb you want is simply 'put'.

The translation would be: Where should I put that? The construction of the sentence follows the same word order here.