Should I change thai baht on Patong beach Phuket or here in Singapore before I leave?
It might be a good idea to have a little bit of cash on you before you arrive in Thailand - just is case. However, you can just as easily get cash at an ATM at the airport in Thailand (if you have one that you can use internationally) But if you need to actually exchange money - then any exchange booth is good too.
I don't totally agree with KK Oz about exchange booths (but hey! we all have our preferences). They are not as bad as it sounds. The place NOT to exchange is at the hotels! That's where the rates are significantly lower than the exchange booths.
Have a great trip and enjoy Phuket. I have not been there since the tsunami and I would love to ge there again this year and see how things are now.