I live in Dublin, and am specifically thinking of places like Rathmines, Ranelagh, and Drumcondra as suburbs. These places have a more suburban character, with a distinctly residential feel, but are only 2-4 km from city center. Dublin's not a big city, though. You are correct in your examples from large American cities, but I'm not sure they're broadly applicable outside the US.

The US is, of course, different and drastically distorted thanks to building everything for cars instead of people. Human scale "cities" aren't 60km across. I'm not even sure they deserve to be called cities, but are rather a new sort of urban-ish agglomeration.

Before moving here I lived in Santa Monica. It was about the best I could do for finding a place where I could walk to anything interesting, and even then we're talking about fairly lengthy walks. When you get around by bike, walking, and public transit your sense of scale changes drastically, and you realize that most US "cities" built since 1920 are sprawling fields of asphalt with a building sprinkled here and there. That being said, I'm glad I was in Santa Monica where I was at least able to cycle to a reasonable number of things, and not, say, Northridge, or another place where the parking lots are almost as big as Dublin's downtown.