the usual expat enclaves are:
orchard and its surrounding areas (tanglin, scotts, paterson and further - river valley; balmoral, chancery, newton, novena)
bukit timah, upper bukit timah, clementi,ulu pandan and holland areas
east coast (katong/siglap and surrounding areas)
the heartlands (HDB estates - apartments) normally within walking or 5 minute feeder-bus distances from a bus-stop or MRT station. (the nearest ones to orchard are toa payoh, ang mo kio and bishan)
other residential burbs with houses (mostly local residents) - thomson, upper thomson, sembawang, seletar, serangoon gardens etc.
not sure about the chinatown area. clarke quay and riverside areas (nearer downtown business area - shenton way) apparently have new condo developments there too.
there are bus-stops and mrt stations (as well as cruising cabs) almost everywhere in singapore so nowhere is really inaccessible or inconvenient.
hope that helps in your house-hunting. 