There is Pulau Ubin, an offshore island for cycling. Not a big island but well it's a nice getaway. You can rent the bicycles on the island. Take a ferry from Tanah Merah Ferry Terminal.
You can also check out the farms in Lim Chu Kang area. There are fish farms, goat farms and veggie farms.
East Coast beach/park is a nice place for BBQ, cycling and roller blading. You can rent a BBQ pit from the http://www.nparks.gov.sg/cms/index.php?option=com_visitorsguide&task=parks&id=14&Itemid=73
There is also Universal Studios on Sentosa Island.
Check out also Bukit Timah Nature Reserves. Though small, you might spot monkeys, huge spiders, snakes and even komodo lizards at times.