Greensboro Symphony Youth Orchestra (
http://www.gsyo.org/); Winston-Salem Symphony Youth Orchestras Program (
https://www.wssymphony.org/education/youthorch/about/) ... don't know which is better. There is a lot of Reynolds (tobacco) money still percolating through Winston-Salem that has and continues to fund all sorts of artistic endeavors including music. On the other hand, UNC-Greensboro has a fantastic undergraduate and graduate music school.
For your older child, the EMF (
https://www.easternmusicfestival.org/) is a music festival that happens for several weeks every year in Greensboro, mostly on the campus of Guilford College. It is a FANTASTIC opportunity for talented and ambitious young musicians to dedicate several weeks to lessons, rehearsals and performances with world-class instructors - this draws young musicians from all over the U.S and some from overseas. There are also a lot of concerts (some $, some free) that the general public can enjoy.
For Christian schools,Bishop McGuiness High School (
https://www.bmhs.us/) in Kernersville;
Our Lady Of Mercy Elementary (
Our Lady of Mercy Catholic School) and St John's Lutheran (Elementary and Middle School,
About Us | St. John's Lutheran School in Winston Salem) in Winston-Salem.
In Greensboro, Caldwell Academy (
https://www.caldwellacademy.org/), New Garden Friends School (
New Garden Friends School - Greensboro, NC)
Good luck with the move ... and say goodbye to snow, pretty much.