I have also been trying to find what we would call back in the states a nice "coffe shop" or "diner" for breakfast, but no luck so far. The closest I have found is Rocky Master on Orchard Road, opposite Orchard Parade Hotel. It has something called "American Breakfast" which is more what I would call a hybrid "British/American Breakfast". Eggs, Tomato, Cucumber, Toast, Hash Browns, Turkey, Bacon, Coffee and Juice for S$9. Quite a bargain if you can eat that much! I consider the coffee very good, but of course everybody has a different opinion about their coffee
I believe they also have outdoor seating.
I have since given up and started having Roti Prata and curry for breakfast - when in Rome...