Where are you flying in from and what airline if you do not object to sharing?
If on UA from the US via any of their gateways I know of you will end up at terminal 1 and arrival will be very late (about midnight). How early are you planning on leaving the next day? Remember there is an airport hotel at Changi (SIN) but you must get reservations far in advance and it is not a budget location.

With more infor, I suspect others can assist you in defining your stopover if you ask.

Have a great trip...by the way, I am going to take a 2 day run to Phuket during my next 1 week visit to SIN (in April) so your posting is of value to me.