These not-quite-spring days of March can be terribly anxious ones for eighth-graders and their parents, waiting to hear where and if they are matched for a New York City public high school.

Now’s a good time to spin a few fantasies before harsh realities kick in.

Anyone who has already dragged through the full-time job that touring schools entails already knows the first reality: There’s a real supply and demand crisis in this city’s public school system. There simply aren’t enough high quality high schools, leaving kids vying to get into about a dozen top institutions that don’t have enough spots.

And even these very top, highly coveted schools all are beset by budget problems, large class sizes and an inability to provide sufficient guidance counselors, sports, arts and individual attention.

I’ve concluded that the high school I would love to send my two teenagers to in New York City simply does not exist – yet.

During years of exhausting tours, we encountered terrific teachers, ideas, and specialized programs that held lots of appeal. But none of them came together in one building, in one convenient location, with all of the creativity, variety, fun and rigor I would like to see in a high school education.

I was floored by gorgeous facilities and creative thinking at New York City Harbor School, which recently got a boost when U.S. Secretary of Education Arne Duncan came to visit. When we toured three years ago, the school was too new to have a strong academic record or a soccer team, which were both important in my family, and I feared my hard-to-awaken teenager might regularly miss the ferry to Governor’s Island. I loved the rich intellectual culture and exciting teaching at the Manhattan campus of Bard Early College High School, but we all had mixed feelings about college level courses and heavy homework loads so early.

Beacon had strong arts and a great community service ethos, while managing to avoid thedistasteful drilling for New York State Regents exams. The class sizes were too large, though, and the facility was not without its challenges. Lines just to get into the tours were absolutely daunting, as were acceptance rates.

The specialized high schools have some great programs and reputations, but entail grueling entrance exams, and can be huge and impersonal. Recent scandals at Stuyvesant and now Bronx Science are also troubling.

When I dream of a perfect high school, I’m not envisioning a suburban, private or charter school. I am talking about a fantasy New York City public school that takes all comers, with a diverse student body, small classes and teachers who get to know their students both by name, ability and interest. By ability, I don’t just mean performance or growth on standardized test scores.

The fantasy high school would feature an atmosphere of kindness, tolerance and respect. It wouldn’t dream of starting classes before 9 a.m.; at the very least would offer a choice of later start times for sleep-deprived adolescents.

This high school would have actual athletic fields for sports teams, so that a soccer team could actually kick the ball somewhere other than a gym or crowded public park, and multiple sports could be offered at the same time. The school play would have parts for kids without agents and previous Broadway experience.

There would be no rejections and wait lists for advanced placement courses. There would be plenty of guidance counselors on hand to help with the usual array of teenage crisis, plus provide practical tips and advice on college admissions. There would be many interesting electives to choose from, and a huge emphasis on learning instead of simply memorizing. There would be less testing, more writing and more discussion – of history, current events, ethics and values.

Foreign language offerings would be varied and available. Math and science teachers would be so excited about topics like physics, chemistry and calculus that kids would actually want to go to class. There would be no gangs, no violence and few disruptions.

This “perfect,’’ high school is something I’ve given a great deal of thought about, both personally in two recent years of touring high schools, as well as in my professional life, which takes me into dozens of high schools throughout the U.S.

As it turned out, both of my children now attend a large, specialized arts high school with plenty of challenges but lots of wonderful qualities. There’s not a day I’m not grateful for the tremendous experiences they’ve had there. There are many things I still wish for, but the trade-off for a rich arts specialization has been absolutely worthwhile.