I travel a lot and get my hair cut in many different places as a result. Jack's is the best.
Most importantly, the quality of the haircuts you receive in Jack's is excellent. The individual hairdressers are each very good, and if you're lucky enough to bag Jack himself (not always easy) then you'll have the haircut of your life. Everyone at Jack's does great cuts to your specifications, but the real treat is having Jack decide for you what's best. He's excellent at that.
If you care about the experience itself, there's friendly banter and a super-relaxed vibe. Whenever I'm in London, I make a point of going to see Jack.