I agree that Nagasaki is a fine choice but for an itinerary that goes from Nagoya to Fukuoka and back up to Tokyo, it is probably a bit of a reach. Unless, that is, the OP wanted to fly that last leg from FUK to HND or NRT.
I think the Centrair airport in Nagoya is a great place to arrive in Japan. I only wish my preferred airline still used it. However, there is not really much to see in Nagoya. Since the trip to Kyoto is less than 2 hours, I'd just go straight to Kyoto without the overnight in Nagoya.