Alexandra McDaniel, 29, grew up in Scottsdale, the affluent suburb north of Phoenix. As she and her fiancé, Cameron Smith, 32, began their search for a home early this year, she hoped to live close to her parents, and near her job at a fashion retailer. Mr. Smith was intent on finding an area where Ms. McDaniel could safely walk their dog alone at night.

Mr. Smith is a data analyst at Amazon. Together, he and Ms. McDaniel earn roughly $200,000 a year. They figured they could afford to pay as much as $550,000 for a home, though they aimed lower.

But as they sat in a conference room on a recent morning, their Realtor, Curt Johnson, projected a map on a screen that forced them to downgrade their expectations.

He had searched for houses with small pools and at least three bedrooms priced at $475,000 to $575,000. Scottsdale had no listings. The half-dozen properties he had found were scattered about 15 miles away, and beyond a freeway.

“It’s a lower-income area,” Mr. Johnson said, adding that it had “a higher crime rate.”

He drove the couple out for a look. The first two homes had tiny yards unsuitable for their dog. The third place had a huge yard and a wide-open kitchen, but the asking price was $599,000. The next one was similarly priced, and the neighborhood felt seedy. The last house was within their budget, but alongside an apartment complex whose balconies looked directly into the yard.

As they drove back to Scottsdale, they struggled to make sense of their situation.

“We have great jobs,” Ms. McDaniel said. “We’re doing exactly what we were told to do, and it doesn’t work.”