If parents don't mind you guys in the room together, can do it
in the bedroom. If not, then have to look for something
outside.....
There are many transit (short time) hotels like Hotel 81, etc which
can be quite fun. Around S$20 for 2 hours....S$10 for each
additional hour. Not everyone likes to go to these hotel branches
at Geylang, but there are so many outside the Geylang area.
You indicated that you don't like public places....or else there
are many places where you can have lah. Some find it exciting, some
find it uncomfortable.
(By the way, I'm not a kid still living with parents.....but I
speak from past experience).