Sunger Buloh is a choice:
http://www.sbwr.org.sg/

Chek Jawa of Pulau Ubin is another Choice:
(map of Pulau Ubin: http://www.nparks.gov.sg/nparks_cms/cms/cmsmgr/data/6/Ubin_Map.jpg)

LimChuKang Mangrove is a third Choice:
(map of LCK mangrove: http://mangrove.nus.edu.sg/guidebooks/text/1006.htm)

Pasir Ris Park is a fourth choice:
(map of PR park: http://mangrove.nus.edu.sg/guidebooks/text/1017.htm)

I personally think, Labrador Park and Kranji Nature Trail are good places to visit, too. These two places are more like tidal wetlands, not mangroves, but you can find a lot of funny crabs, lobsters, shells, crawling around your feet
(map of labrador park: http://www.nparks.gov.sg/nparks_cms/display_park.asp?parkid=12
map of Kranji NT, you have to search by yourself.....)