In addition to having to apply for CCW in the same county where you took the qualification test, when it comes time to renew, you have to renew in the same county that issued it. If you switch counties, you have to go through the training and test again.
In my case, I took the Front Sight Course in Pahrump, which included the NV CCW test. So, I had to apply for my permit at the Nye County Sheriff's Station. When I renew, I need to go the the Nye County Sheriff's Station again.
For non-residents, NV requires the applicant to appear in person at least once in the process. So, you can either submit your application by mail and pick it up in person when it's ready, or you can apply in person and they will mail it to you. Most people I think choose the latter, since timing your trip around your permit being ready is more difficult.
NV residents are required to apply in the county where they live. Maybe it's easier to just buy a house there? [ /sarc ]

So, if you're staying in LV, it's probably more convenient to visit the Clark County police station. That means you have to take the qualification test in that county, too. If you go early enough, it might not be that long of a wait.
You probably won't have slept the night before anyway!

Those were the rules when I got my permit. Things might have changed, but the last time I looked up their rules a few months ago, it was the same process/restrictions.