You only really need a few days to see Singapore IMO. There's a huge botanical garden thing behind the Sands hotel. May be worth booking a night there actually and enjoy the swimming pool on top. Chinatown in Singapore is basically two small streets. You can see it in about half an hour. The Sands is on the waterfront more or less, so you can spend a day ambling around there but once you've seen it there's not much left to do. There are some interesting malls around (one mall for example has a floor full of camera shops and another floor full of tech gadgets such as USBs) so if you fancy wasting time shopping, Singapore isn't a bad place to do it. Easiest way around Singapore if you want to explore is the subway. Taxis are about the same as the South East in UK.
Thailand would be good, but it can be hard work at times. If you're looking at Phuket, consider Ko Phi Phi. Alternatively, you have the islands on the east such as Ko Samui.
Bangkok is very full on, so unless you definitely want to see it, I'd avoid it if you want to relax. Consider looking north towards Chang Mai and Chang Rai although that will likely require an additional flight to get there from Bangkok. The White Temple is supposed to be interesting. There's also an elephant sanctuary near Chang Rai I think. Bangkok is good for going to the new developments and shopping centres. The touristy areas are incredibly busy. If you go, make sure you decide what you want to do before landing. Getting a cab will be quickest.
Thailand would be good, but it can be hard work at times. If you're looking at Phuket, consider Ko Phi Phi. Alternatively, you have the islands on the east such as Ko Samui.
Bangkok is very full on, so unless you definitely want to see it, I'd avoid it if you want to relax. Consider looking north towards Chang Mai and Chang Rai although that will likely require an additional flight to get there from Bangkok. The White Temple is supposed to be interesting. There's also an elephant sanctuary near Chang Rai I think. Bangkok is good for going to the new developments and shopping centres. The touristy areas are incredibly busy. If you go, make sure you decide what you want to do before landing. Getting a cab will be quickest.