If you can afford it, you should buy a house in a good school district whether you have kids or not, right?

Maybe not anymore.

Conventional wisdom has long equated good schools with higher home prices and better property value retention and appreciation. Conventional wisdom isn't so much wrong as it is slowly aging out of vogue.

A recent Realtor.com (NASDAQ: MOVE) survey found that good schools are still a key factor for most homebuyers, with 91% saying school boundaries were important and 20% saying they would pay 6% to 10% more for a home in the right school district.

But what people say in a survey and where they're actually moving and paying top dollar for real estate tell two different stories.

American cities are growing faster than their suburbs for the first time in a century and many economists argue that the young affluent pouring back into city cores might actually stay there even after they start families – if they start families.

The great inversion

The term "inner-city school" became synonymous with gang activity, drugs, guns, illiteracy, teen pregnancy, and dropouts in the 1980s, the heyday of the suburbs. The affluent fled city centers into ever more far-flung suburbs, leaving rundown cheap housing for the poor and non-English-speaking immigrants in the city centers.

While the best schools grew up around the neatly manicured grass lawns and tidy strip malls in suburbia, the schools in the hearts of American cities saw declining populations and kids with every possible economic and social hurdle, resulting in some pretty grim statistics for city schools.

Most still have bad reputations, but that's going to have to change – and it is – if cities want to retain the robust populations of young professionals they have cultivated over the last 20 years and if they want to continue gentrifying and pushing their poorest residents to the suburbs.

Urban populations grew by 12.1% between 2000 and 2010, outpacing national growth of 9.7%. Some of the country's most popular cities grew more than 50% over the same period, according to the U.S. Census report.

Just between 2010 and 2011, city populations grew 1.1%, while suburbs grew 0.9%, the first time since the early 1900s that city growth outpaced suburban.

Cities are drawing the young, talented, creative, and affluent. A survey from real estate firm Robert Charles Lesser & Co. found that 77% of the 86 million Millennials want to live in an urban core.

That desire to live in a city is driving rapid real estate appreciation in urban areas.

Trulia (NYSE: TRLA) economist Jed Kolko found that urban home prices rose 11.3% year-over-year, while suburban home prices climbed 10.2%. High-rise developments saw an 11.9% gain and urban real estate in the most diverse neighborhoods appreciated 14.3%.

Referred to as the great inversion by some economists, the shift to cities has pushed the poor and the new immigrants out to the suburbs. The suburban poor increased 25% between 2000 and 2010, five times faster than in cities.

So, how long before the term "suburban schools" has the same ring that "inner-city schools" once did?

Families

Conventional wisdom would have us believe that the young professionals who have filled city apartments will soon begin marrying and having babies, which inevitably calls for a move to a big house in the suburbs and a minivan.

But there's a chance this car-loathing generation might buck the century-old trend toward grassy yards in favor of being able to walk to their neighborhood preschool or library.

The rise of school choice and emergence of charter schools means there are more options for urban parents. And cities, eager to keep their new population base, are doing what they can to support public school improvements and expansions.

Even if the Millennials who start families do opt to leave the city, the exodus is likely to be much smaller than you'd expect. There might not be so many children in this next generation.

More than half of American households had children under 18 living in them 50 years ago. Today, fewer than 43% have children with 29% of American households including childless couples and almost 28% living alone.

In the suburbs

The best schools today tend to be near the newer and wealthier developments. Some established neighborhoods are known for their good schools, but historically more affluent families move to the next new suburb and build up good new schools, leaving old ones with dwindling populations, vacant grocery stores, and wrinkly old grandparents on fixed incomes behind.

But those older suburbs are closer to the city and they are usually more walkable. The houses have "character," the yards are big, the streets have trees, and the areas have soul. The houses are relatively affordable and the people who lived in them are dying or moving into retirement homes – making them available for the first time since they were new 50 to 60 years ago.

Perhaps that's why midcentury modern architecture and design is so in vogue now.

But those neighborhoods aren't where the best schools are located. They're where schools have closed and left vacant shells and empty parking lots for weekend flea markets.

And they're perfect for the charter schools out there hunting for good real estate.

The young people, increasingly keen on living in walkable and mixed-use communities, are revitalizing those areas in a time of community activism. Young parents who don't want cookie-cutter houses in the corn fields will fight to get good educations in the communities where they want to live.

So, how important is it for appreciation to buy in a good school district? Ask one of the 86 million Millennials you know.