When you think "young and rich" in the United States, chances are two cities come to mind: San Francisco and New York. You'd be right that those places have a lot of wealthy millennials, but they don't take the top spot, according to Zillow.

The No. 1 city for millennial-headed households earning incomes of $350,000 or more? Arlington, Virginia, in metropolitan Washington, D.C., according to the real estate database company.

"Whether they made their money lobbying lawmakers at the Capitol or cashed in on a tech IPO, rich millennials are clustered in cities where there are lots of high-paying professional jobs," reads a post today on Zillow's Porchlight blog. "Tech hubs made the list, but young people are doing well in older job markets, too."

San Francisco -- "synonymous with high-paying tech jobs and a tight housing supply," Zillow notes -- came in at number two on the list, and neighboring city of Oakland at number nine. Silicon Valley suburb Sunnyvale, where the headquarters of Yahoo is located, came in at position four.

To Zillow senior economist Aaron Tarrazas, the data shows how some locations and career fields contradict the widely held notion that millennials -- defined by Zillow as age 34 and younger -- are struggling "to find good jobs and affordable homes."

Zillow's list contains the exceptional cases where "young adults have done very well -- particularly those clustered around job centers for booming, well-remunerated industries, such as tech, finance, and law," he said in a statement.

"With substantial disposable incomes and often limited family responsibilities, these financially well-off young adults have contributed to new demand for luxury apartments and urban services such as restaurants and bars."

The last point about demand for luxury apartments could strike a chord with residents in the Silicon Valley area. As median income has risen in places like San Francisco and, increasingly, Oakland, so have housing costs. San Francisco home values increased 14 percent over the last year to a median value of roughly $1.1 million, according to Zillow. In Oakland, values climbed almost 18 percent to $586,800.

The rising home values -- and rent prices alongside them -- are associated with displacement of less affluent city residents who can no longer afford area living costs.

Here is Zillow's complete list of the top 10 cities for percentage of millennial-headed households that earn more than $350,000 a year.

1. Arlington, Virgina.  8.7 percent of millennial households

2. San Francisco 7.8 percent of millennial households

3. Huntington Beach, California. 5 percent of millennial households

4. (tie) Sunnyvale, California. 3.9 percent of millennial households

4. (tie) Seattle. 3.9 percent of millennial households

5. Pasadena, California. 3.3 percent of millennial households

6. Denver. 3 percent of millennial households

7. Cambridge, Massachusetts. 2.9 percent of millennial households

8. (tie) Washington, D.C. 2.8 percent of millennial households

8. (tie) New York. 2.8 of millennial households

9. Oakland, California. 2.6 percent of millennial households

10. Jersey City, New Jersey. 2.2 percent of millennial households