Help with choosing a private school for my daughter

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Me and my family will be relocating up north and the location will be based on the school we put our daughter in.
We will be placing her in for sixth form but late entry as a day student. She is very academic but would also like a school with very good extracurriculars such as sport, music and anything different like horse riding.She is also a person of colour so a school with no racism is definitely key and preferably a larger sixth form size as she will be joining late.

Facilities wise - a nice swimming pool and a pretty estate and nice classrooms

Here are the schools we are considering:
Hillhouse
Woodhouse grove
Yarm
Ackworth
Bootham
Pocklington
Fulneck
Silcoates
Rishworth

Any suggestions would be appreciated. Thank you

Have you looked at the proportion of borders?

and whether even space for a late entrant

you mention everything aside what she actually wants to study!!

Firstly you need to find out which ones have got space and the admissions process. I personally wouldn't base a house move for 2 years of school. Choose the school you want and preferably a boarding school so location of house won't matter.
Also which school offers the A levels choices that she wants.
Yarm is a great school in terms of results and facilities but just out of our area so didn't consider it and therefore no experience of it with regards to diversity. All I would say is that NE is generally low levels of ethnic diversity so that may rule Yarm out.

Avoid Rishworth like the plague. Terrible school with very "cliquey" environment. Lack of continuity in teaching staff and almost no reward or encouragement unless you are a high achiever / very sporty. I had to remove my dd due to all the above and some low level bullying that was never dealt with
Good luck with the other schools