For my money, of all the spin-offs and sequels and stuff, Deep Space Nine came the closest to recreating the spirit of TOS.
Your milage may vary.
My mileage is similar, but it's not so much the spirit of TOS that DS9 recaptured, but the mandate of TOS to do storylines that actually had some meat on the bones and tried to challenge the audience to look at, and think about, things in a different way; certainly better than TNG ever did, with a few notable exceptions.