As an American, I don’t think of the suburbs when I think of rich people. I think of what’s left of our middle class just trying to do their best. Many of them probably have negative net worth when debt is considered. But they need public schools, they need big (relatively) affordable housing, they need strip centers with the same 5 restaurants every exit of the highway. When I think of wealth, I think of mostly inner city old money areas or neighborhoods that have had gentrification (not underway). They live near their work/business, near poverty even, but they don’t commute far because they value their time and they will pay for private schools and create their own sports leagues and stuff for their kids and private security to keep out the riff raff. These areas were probably a far out suburb 50-100 years ago but a city grew around them but their wealth was enough to isolate themselves. That’s where the wealthy people live.

It varies by location and by what we mean by rich. In New York, for example, you're totally right. But for most of America the model is country club + suburb, 6,000 sqft house with a pool, big public school district that is very well funded, SUVs, &c. for the "rich".

And in some cities you actually have both. Where I live we have these big, wealthy suburbs (New Albany for example), Delaware County in central Ohio is one of the top countries by income in the whole country - all suburban. Yet we also have some absolutely fantastic and premier neighborhoods in the Columbus area with prices to reasonably match given the scarcity of actual neighborhoods and such, though I actually think the homes in these areas are a bit under-priced and the large suburban homes a bit over-priced.

It’s even more extreme in the Bay Area. While San Francisco is a job center, there are also major suburban job centers such as Palo Alto, Cupertino, Mountain View, and Sunnyvale. The problem is living close to work is painfully expensive for all but the most well-off employees. A Google executive could comfortably afford a nice house in Los Altos or Palo Alto and have an easy commute. A Google engineer could commute from Fremont or Pleasanton, which would be grueling in a car, but is comfortable on a Google shuttle bus with leather seats and WiFi. But if you’re a teacher working for a school in Mountain View, my condolences. If you want to afford to buy, you’re looking at a grueling commute from either a middle-class exurb like Tracy or from a high-crime, impoverished area like East Oakland. Even renting an apartment closer to work would be daunting in terms of cost.

Eh, the wealthiest in America mostly live in spacious suburbs. They aren't very city-like, but they're not the same suburbs as GP mentioned either. In every wealthy metro, there will be a couple areas that the wealthiest coalesce around.

Think Hillsborough/Atherton/Palo Alto, Carmel IN, Newton/Brookline MA, Beverly Hills, Greenwich County CT, River Oaks in Houston, Boulder CO, Scottsdale AZ, etc