No. i don't recommend you staying at Geylang. its not a fun
place or anything, you can visit it at night for the local food.
But staying there during your whole stay in Singapore is not
really pleasant or memorable.
Since you're loaded, i suggest you getting a hotel at orchard.
EG, ( York hotel ). its nice and its close to many malls and its
really convenient to get to anywhere. ( although i'm sure you'll
most probably take the taxi. )
Here are some of the many interesting places i recommend you to
visit During your trip.
Sentosa , esplanade , Merlion park near Singapore CBD ,
Clarke Quay , Boat Quay , Sir Stamford raffles statue ,
Pulau ubin island ( you need to take a ferry to the island)
,
Singapore zoo , Jurong bird park.
Have fun. =D
You forgot pulau tekong....