I have a level 16 Nidorino and a Moon Stone. Should I use it right away, or should I wait until Nidorino gets to a certain level? Would it make any difference?
There's no easy answer to this. Evolving to Nidoking will increase its stats by a fair amount, but it will not be able to learn as many moves from level up. Compare these two lists:
If you're not interested in the moves Nidorino would learn via level up, there's no reason not to evolve it immediately.