A multimillion-dollar home may come with sweeping views and lavish amenities — but a top public school rating isn’t necessarily part of the package.

The New York-Newark-Jersey City metro ranks ninth among the most expensive luxury housing markets tracked in Realtor.com’s September luxury housing report, with the priciest 10% of listings starting at $2.62 million.

Yet public elementary schools assigned to those properties average 6.7 out of 10 on GreatSchools, placing the metro among the bottom 10 of the 43 markets studied.

The findings suggest that buying at the top of a housing market doesn’t necessarily mean getting a public elementary school rated among its state’s best.

GreatSchools ratings compare schools with others in the same state, rather than using a single nationwide academic benchmark.

According to GreatSchools’ published methodology, ratings reflect state test results and academic progress relative to other schools in the same state. Realtor.com averaged the overall ratings of public elementary schools assigned to luxury listings in each metro.

The New York result covers the broader metropolitan area, including communities in New Jersey. It is not a rating of all New York City public schools.

Realtor.com examined markets that averaged at least 500 million-dollar listings over the previous 12 months. Within each metro, it defined luxury homes as September listings priced at or above the local 90th percentile.

Each property received the average GreatSchools rating of its assigned public elementary schools. Those property-level scores were then averaged across the market, excluding homes without an assigned school rating.

Naples-Marco Island, Florida, led with an average school rating of 9.3. Its luxury listings started at $3.69 million, making it the third-most-expensive market in the analysis.

Crestview-Fort Walton Beach-Destin, also in Florida, followed with a 9.1 average and a $2.87 million luxury threshold.

Closer to New York, Bridgeport-Stamford-Danbury, Connecticut, ranked third for school ratings at 8.5, with luxury listings starting at approximately $3.6 million.

But some markets with substantially lower luxury price thresholds also stood out.

Jacksonville, Florida, ranked 11th for school ratings, averaging 7.8, despite a luxury entry point of $900,388. San Antonio-New Braunfels, Texas, placed 15th with a 7.4 average and a threshold of $780,487.

Both thresholds were below the national luxury entry point of approximately $1.2 million.

“Some really affordable areas really popped out here in the top 15,” Smith said. “That was really intriguing to me.”

Their placement indicates that schools assigned to luxury listings can rate highly against their state peers even in markets where the top tier of housing costs considerably less.

At the other end, Kahului-Wailuku, Hawaii, had the second-highest luxury threshold, at $3.79 million, but the lowest average school rating, at 5.0. Urban Honolulu followed with a 5.7 average.

The analysis also excludes private schools, school-choice programs and lottery-based admissions, capturing only part of the educational picture families may consider when purchasing a home.

School ratings are often a starting point for buyers, but other priorities can carry more weight, said Seth Keslow, an associate real estate broker with Compass’ Keslow Hurwitz Team in Westchester.

“Most of my clients rely on their online searches to obtain general school ratings,” he told The Post.

He added that a home’s location within a town and proximity to work or loved ones can matter more than its school district.

“In any event, the definition of a ‘great school’ varies from person to person,” Keslow said, adding that online ratings are “usually a starting point but not always an ending point.”

Strong school ratings weren’t a shield against falling luxury asking prices, either.

Despite its third-place school rating, Bridgeport-Stamford-Danbury’s luxury threshold fell 15.6% from a year earlier — the steepest decline among the 10 most expensive markets.

New York’s threshold dropped 11.3% annually, although it rose 1.1% from August.

Nationally, the luxury entry point fell 3.6% to $1.199 million marking the 30th consecutive month of year-over-year declines. The threshold now sits 14.1% below its May 2023 peak.

Those figures measure listing prices rather than completed sale prices — and, like the school ratings, offer buyers one piece of a much larger decision.