I just thought I would express my own opinion about this. The OP's original request was, what's available at Changi Airport hotel-wise in the middle of the night. It's not clear to me that he/she/they are necessarily looking to go into town, rather a place to put their heads down for an hour or two was what was wanted. Granted that going into town is a choice, but my view is that Mustafa Centre is better appreciated during the daytime especially for first timers.

To the OP, I neglected to mention in my earlier post that there are budget hotels in town, but given the existence of free sleeping spaces at Changi Airport (airside), if your objective is to get some sleep, then there's not much point to leaving the airport.