I think it would be interesting to visit a time of change--an alliance with the Klingons, Kirk 'dead', and a whole new era of exploration opening up.
Yeah yeah yeah. Back in the 80s this was my dream scenario for a new Star Trek series. Something set "now" relative to the orginal series, ie 20 years later (now 40 or 50 years later), and dealing with the time when the Klingons went from being enemies to allies. Uneven allies, where you wouldn't know what to expect from any Klingon encounter: some Klingons would be for alliance (good guys) and some would be against (bad guys).
Then TNG came along and ruined everything.
That's still what I most want to see from a new Star Trek series.