How close can you install outdoor electrical outlet to water faucet?

The NEC does not specify. Outdoor outlets are required to be GFCI protected so, in theory, if all works properly, it shouldn't matter.

But I wouldn't place the outlet below the faucet under any circumstances.

And I wouldn't place it in close proximity, say, less than 2 feet apart. But this all depends on how convenient it is and what appearance you are looking for.