If you want a shower and nap in SIN there is a transit hotel right in the terminal; it's within the secure area. It costs around $60 for six hours (the minimum you can book). Info and links are on the Changi Airport website. There are also a couple of 24-hour places to eat. My favorite is a place up on the mezzanine level where you can get decent wonton soup.

SIN is ranked one of the best airports in the world and is my own favorite, but I wouldn't consider 6 hours there in the middle of the night as a great birthday celebration.