I thought the same thing at first, but her DD is only 11 years old and in 8th grade. She could have a 12 year old in high school next year.
It's unusual but not that rare. I know more than one kid who was that age.
NYC is 5 hrs away i am looking for specific namesnof schools to look at
There are just tons, I'm not even sure how to narrow it for you - I mean literally I could name 20 off the top of my head.
However, as a couple of us noted, you're pretty much at or beyond the deadline for admissions for next year for many, many schools (not just here but many places).
All the specialized high schools here, which are some of the top in the nation and have incredible programs (and are free of charge to attend), are testing this weekend. So those, like Bronx High School of Science, Stuyvesant, etc., are all out.
As for the others, a good school is a process. There are admissions packets, ISEE/SSAT or etc., recommendations, etc., and you're past the date for many schools (even if you could sneak under the test or full app deadline, a lot have step deadlines for recommendations, etc.).
As well, if we're talking about private schools here, what you'd look at depends on what tuition you're prepared to pay. The top notch privates here run in the neighbourhood of $30,000-40,000 per year. And, again, even if you're willing to pay that, you're running out of time very quickly.
I know about schools here so can't speak to other places but for here - we have a plethora of crazy good, challenging, top-notch schools with exceptional programs. You need to start applying like, yesterday and take the ISEE/SSAT/TACHS/etc., or their proprietary exam if possible, as soon as possible to even think about squeaking in.