Kirsten and Theodore Bruckbauer never planned to leave the Chicago area.

They were both raised in the region and had owned a home in Evanston, Ill., just outside the city, since 2020. Their two sons, 10 and 5, biked to their friends’ houses around the neighborhood “without giving it a second thought,” Mr. Bruckbauer said.

Late last year, though, Mr. Bruckbauer, who works in cybersecurity, was approached about a job that seemed almost too good to be true. He was excited, but there was a catch: The job was in New York.

“We were not going to go to New York,” Mr. Bruckbauer, 45, recalled thinking.

Still, conversations with the family and the company continued. And over time, he said, the opportunity “seemed like a better and better fit.”

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“There are moments in your life, in your career, that you just can’t say no to,” said Ms. Bruckbauer, 46. “It was a huge, huge opportunity for Ted.”

The couple visited New York City in February to see how they felt about the Upper East Side. It was not a match. The boys, they realized, would not be biking freely around the neighborhood.

At the suggestion of Mr. Bruckbauer’s future colleagues, and upon seeing the ease of the Metro-North Railroad, the couple decided to focus their search in Westchester County, N.Y. A garden, a town center within walking distance and a guest suite for the family and friends they left behind in Illinois were among their priorities. Good schools in the area were imperative.

They also needed easy access to the city, since Mr. Bruckbauer’s job required him to be in Manhattan four days a week. Ms. Bruckbauer, who works remotely for a product research firm, was more flexible.

They hoped to keep their budget under $1.8 million, but they were willing to go higher for the right house.

“We love a small house, larger lot,” Ms. Bruckbauer said.

What they did not want was a project or a pool.

The family worked with Dee Coffey, a real estate agent at Compass who, knowing they needed to be settled in before the start of the school year, “injected this urgency” into their search, Ms. Bruckbauer said.

The Bruckbauers flew out twice in April, rented a car and “drove to almost every train station in Westchester,” Mr. Bruckbauer said. They were startled at how quickly — and how far above asking price — homes were selling.

“It was a steep learning curve for us to feel the dynamics of the market out here,” Ms. Bruckbauer said.

Among their options:

Set on a 0.77-acre lot, this five-bedroom, three-bathroom home in Irvington, N.Y., had a garden brimming with greenery and an enormous window in the family room looking out on it. A brick fireplace and beamed ceilings added to the cozy feel of this 1965 home, which had enough space for an office and a guest room over its 3,208 square feet.

The commute to New York City was just over an hour, about the longest Mr. Bruckbauer could bear. The house didn’t have air-conditioning, a concern for summer. A pool was hidden up a set of stone stairs behind the garden’s dense greenery. It was listed at $2 million, with $43,378 in annual taxes.

This 1953 colonial-style home had four bedrooms and three and a half bathrooms across 3,361 square feet. Situated on a 0.31-acre lot in Sleepy Hollow, the house featured cathedral ceilings, an open kitchen with granite counters and plenty of space for a home office and guests.

Listed at just under $1.6 million with $34,085 a year in taxes, it was comfortably within the Bruckbauers’ budget and the neighborhood was appealing. But the train ride to Grand Central Terminal could take over an hour and there was more street noise than they would have liked.

This 1915 colonial-style house in Hastings-on-Hudson had four bedrooms, three bathrooms and views of the Hudson River. Perched on a hill, the house had 2,736 square feet of living space on a 0.34-acre lot and featured French doors and high ceilings.

Ms. Bruckbauer was drawn to the greenery surrounding the house, but parts of it felt old and would need to be updated. It was listed at $1.7 million with $34,034 in annual taxes. Its proximity to New York City — the closest of the three — was a draw.