I've been road cycling in Singapore for a few months now, I thought I'd add some info.
The two biggest road cycling groups I have ridden with are:
Both are great and have a range of ride to suit most levels. I'm know there are other groups.
East Coast is great for a nice flat ride. Stay on the service road, not the bike path (too many bladers etc.). You can ride around Changi airport and back, loop is around 40km. Weekends are better as there is less traffic around the loop.
Most group rides take place around the "Mandai loop". Groups meet at the Long House hawker centre and set off from there. The Long House seems to be the focal point for roadies. Last Saturday there were about 150 roadies there at 7am! Lot's of "blingin'" bikes!
Ride early to avoid the heat and traffic and drink lots. If you see a fat bloke rollin' in a "Marmite" jersey be sure to say hello - it's probably me!
p.s. I never ride without a lid here, the drivers are not as cycle aware as the UK.