(I am not home so I do not have my Japanese Keyboard installed sorry )
The ni marks the target of a transition. The question therefor is more like -> What do you want to be (transition to) or What do you want to change it into? (active transition caused by the speaker applied to something)
Consider these examples: rainen nihon ni iku koto ni shita -> I made it so I go to Japan next year (I decided to do it, I changed it into being this way) - the wo is implied here and can be unerstood as the "situation" or "circumstances" for this example.
rainen nihon ni iku koto ni natta -> It was decided that I will go to Japan next year (Things changed naturally, It was out of my control)
The second one (B) uses suru which implies that there is an accusative object involved that has to be inferred from context. It is not grammatically wrong but illogical without prior context.
If you want to say "what do you want to do" you would use "wo shitai no". wo marking the accusative object of what we are "suru"ing.
大人になったら、何にすたいの？ would therefore mean "When you grow up, what do you want to make it into?", which doesn't really make sense (at least not without other context).
As バカ外人 mentioned, if you wanted to ask "what do you want to do?" instead of "what do you want to make it into?", you would use を instead of に as the particle.
You can check the grammar pages on Renshuu for なる and にする for more information.
Thank you. Even as I wrote the question, I figured that 何をしたいの would be the correct version involving したい. Thank you both for helping me clear it up in my mind!
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