Spent a few weeks in Singapore living with relatives.
Road cycling:The car is king and you really need your wits about you – despite the fact their road systems (and conditions) are light years ahead of ours, nothing has been designed with the bike in mind and cyclists are generally treated with contempt out on the road. I wouldn’t judge as very safe for the uninitiated unless riding in a group. I’m sure there’s cycle path stuff down near the beach area although everything they do is very heavily policed so expect to get pulled up for any transgressions;-)
mtb: There’s a formal mtb trail centre @ Bukit Timah (getting there without a car from the town centre isn’t far but you have to negotiate some 6 lane highways in order to do so. I was shown around by a local and there’s a lot of sneaky stuff – some of which is actually very good. Don’t expect a Glentress type facility though.
http://www.mbasg.org/bukit-timah-mtb-trail.html
I know there are forums so look them up and I’m sure some ex pats would be happy to show you the sneaky stuff further into the city. These guys also ride the aqueduct / storm systems for night rides 😉
Also, unless you are acclimatised then forget about doing anything strenuous after midday (in fact first light is ideal)as the heat / humidity can be incredibly draining. I did a couple of solo jaunts and it’s a wee bit spine chilling at first seeing large monkeys snakes and Monitor lizards on and crossing the trails / rustling about in the jungle (it is proper jungle btw) Watch the monkeys btw or rather don’t -eye contact is a no no.
As for the rest – shop til you drop if that’s your thing. Lots of (expensive)eating down at the Quay. If you prefer to get with the locals (which nobody appears to be) then Chinatown and Little India are far more interesting. Everywhere is pretty safe ime.