Suburban in Singapore is hard to come by. In the context of what you are used to, the only "suburban" choices here would be some carefully selected Black and Whites. Those are alse extremely difficult to come by and expensive when found.
The American School is located in the Woodlands, and the northern tip of the center of the island. In itself, it is fairly isolated from the hubub of Orchard Road and the Central Business District. "Little America" as it has come to be known, is a development right next to SAS. It is kind of suburban, as far as mainstream Singapore gets suburban. The houses are either Semi-detached or landed property, but are very close together. Not as crowded as Bangkok, but cozy nonetheless.
Holland Road is another popular expat enclave. It is closer to the CBD and still convenient to Woodlands. There are several neighborhoods there that have landed homes, but again, you are not going to find the type of setting as you would in suburban US.
If you have not already been to Singapore, you may want to come take a look, at least to find suitable housing prior to getting here and to give your wife a chance to look the place over.