25th century of the original timeline. Long enough after everything else so that there would essentially be a blank slate, but still connected to the Trekverse in a significant way.
this. A story set in the mid-25th C. (~2440-2460) would be the best option...it gives you all the benefits of the rich history while allowing you to largely avoid the canonical quagmire of all the earlier eras (TNG-era and 'prequel' eras) in the Prime Timeline.
With the JJverse, they'd never get all the cast to do a small screen series, which is probably a good thing. And it would be self-defeating to try and swing a TV series in the JJverse if it wasn't about Kirk, Spock, and the Enterprise -- that's the whole point.
When Trek goes back to TV, hopefully the powers-that-be will decide that its time for the franchise to boldly go forward again....and that means to the 25th century in the original timeline.
<crosses fingers>