Just thought that I would add that Pulau Ubin is very easy to access - I've transited through Singapore many times and hadn't thought of birding here. Anyway briefly it's $3 each way for the 'Bum boats' (7am-7pm) to Pulau Ubin - operates very regularly and cycle hire $10 cash/day is almost straight off the jetty - easy biking around the island. Only got one call (playback) of mangrove pitta at the spot viator mentioned; no where else. Nice view of grey headed fish eagle at the same spot (a pair of oriental pied hornbills also hung around) and White-bellied Sea-Eagle and accipiters were seen many times. nothing else notable; maybe going back at 7am for a few hrs...
Good luck and Good Birding