SIN is really quite close to the centre of Singapore. A cab should not cost much more than S$ 20. The metro is also quite frequent, and pretty convienient if you don't have too much luggage. The nearest Metro station to the Sheraton is Newton (2 minutes walk away) while for the Meridien you have a choice of Dhoby Ghaut or Somerset stations (both 5-7 minutes walk away).
And all the SPG properties are a quite similar distance from the airport as well.
I wouldn't recommend it, but if you are really really desperate to be near the airport then there is the option of the Changi airport hotel, which used to be a Le Meridien until last year. A 5 minute drive from the airport. But not a SPG prop anymore!