I don't think that human resources is going to know that you failed the NCLEX unless you tell then and I would NEVER tell them.

It is irrelevant since you have now passed it.
As far as interviewing....I'd look the recruiter in the eye and say that you took the opportunity after completing nursing school to work on some personal projects (studying for the NCLEX!) but have finished them and are excited about looking for a job to commit to. Keep it casual and move on in the conversation. You don't owe them an explanation as to why you have not looked for work yet...you might be independently wealthy and just working for fun!