NPAC has the shortest wait time. I got my test date within 24 hours of applying and it was for a few months out from when I applied. It may have been possible to get an earlier date, but I didn't want a date earlier than three months anyway. From what I've read/heard, 3 months seems to be the average wait time for NPAC.
How long it takes to sit for your NCLEX varies from state to state. I wrote the school to find out if there was a way to expedite the process, but they said no. It takes 4-6 weeks after you pass your CPNE to process your graduation and you can't even APPLY to take the NCLEX before you have officially graduated. Then it apparently varies between state to state as to how fast they process your application. Plus you have to take into account NCLEX test site availability. If you graduate EC when on the months when your local schools graduate their GRNs, it could be a while. It will be at least 2-3 months before you can sit for your NCLEX based on the information I received from the school.
Someone here did tell be to be sure and pay the graduation fee immediately after passing the CPNE to help expedite the graduation process.
Some states do allow graduates to take boards before the actual grad date -- Virginia is one of those. I completed my CPNE on June 15, 2008, took my NCLEX on August 6, 2008, and didn't officially graduate until August 15, 2008. Processing you for graduation does take time -- there are thousands of students who attend EC, not just for nursing, who are being processed as well.