Hi, I'd agree with Mobilebucky, better if you can stay somewhere within Changi Airport. Let's look at the math... Meng79 says that you'd get out of the airport at 2AM; for argument's sake I think you can get to the taxi line at 1:30 with a little luck. Even then, if you were to go someplace else - say Joo Chiat area per Meng79's suggestion, you go to bed at 2AM, maybe 2:15, the most sleep you can get is about 3, 3 1/2 hours before you'd have to get up and make your way to Changi airport again. If I follow Meng79's timing of getting out of the airport at 2AM (more conservative than me but pretty reasonable if you don't know your way around Changi), then you'd have even less sleep. In a worse case situation, Changi Airport has quieter areas on the airside where you can sleep. However they are in the open so if you are traveling alone you might not want to do this.

If you decide your best option is to stay at Changi Airport itself, we can give you more precise responses if you can tell us more details, ie, which airline you are arriving on, which airline you are connecting to, whether you have checked baggage to deal with and if you have any status with either or both airlines that you are arriving and departing with.

BTW there's more than one transit hotel - I believe there's one in each of terminals 1 and 2, not sure about 3. However whether they are related to each other, etc I don't know.

(BTW - message to meng79, sorry if it seems I'm picking on you - not intended, just that you had enough hard detail in your post, wanted to offer my interpretation. Apologies, it wasn't personal.)