Depending on your age, there are plenty of good clubs around in Singapore. So if you want to go clubbin there is a very high chance a top DJ is spinning. Else a fun thing to do is to go to Geylang.. or if you are shop minded go to the district where the malls are basically open 24/7.

Like Invisible said you can drop your luggage off at the airport and store it there for just a few bucks!