Not sure where you are staying, but a few things to try
See you have already done Orchard ROAD,
Next, get directions from your hotel and go to No Singboard Restaurant, (around Lorong 19 Geylang) and eat the Chilli Crab,
Go and eat durain
Get some Frog Leg porridge from Geylang.
The Zoo is a must see.
Also be sure to try Bak Kut Teh (get directions from your porter to a good one)
Also try carrot cake and fried oysters. For the carrot cake, take a white one, with Chilli.
Take all of this from a coffee shop / hawker centre.
As to the sites to see? Not so much to look at - if it doesn’t offend your religion do go to the Bugis Street Temple.
By the way, the beach is Tanjong Beach, but the bestest place for nightlife is Zouk - you really shouldn’t come to Singapore without at least having a look.
The housing is not really all that bad - I live in one. At least I don’t have to pay cash for my mortgage (yippee)
The dolphin show is really a waste of time, you will see better at Seaworld in Australia or any of the American ones.
If you are into war history there are a couple of good museums - one on Sentosa.
THe only other place to visit is Haw Par Villa (all taxi drivers know it) - an interesting afternoon walk, taking a look at the gates of hell.
If you have been on the “Metro” (MRT) just take taxis - they are way cheap 
Cheers