I graduated July 2015 and the soonest available date to take NCLEX was in Sept. So...2 months after graduation. I think it's best to take it as soon as possible after graduation.
Update: took test 9/21 and got my results today, I passed and the pearson vue trick worked for me. Unfortunately my file is in enforcement for an old traffic ticket so I don't know when I'll be able to get my license