Good morning Sophia!
What a wonderful choice to make- I made the move from NYC to North Carolina, first renting a wonderful apartment in Cary, NC and then having our home built out in Clayton NC- lots of space for the money- a real change from NYC. And I just helped another couple with two children ages 3 and 2 move from NJ to North Carolina for the same reasons school was extremely important and they purchased a brand new home built to their specifications out in lovely Holly Springs, NC. They came down in August and closed on Dec. 19th. They are very happy with their choice.
I would be more than happy to provide you with details of that area as well- especially noting you are looking for a slower pace of life. As for lower taxes - you will find that in most of North Carolina, Wake County (Raleigh, Cary, Durham, Chapel Hill) will be higher than Johnston County. And in almost all areas you will be able to find a small yard, parks near by and many recreational things to do.
For further information on both Johnston County please view their website(s) http://www.johnstoncountync.org
I do really enjoy the slow pace of Clayton and surrounding areas and their school district (http://www.greatschools.org/north-carolina/smithfield/Johnst
) is still traditional, versus year round as many of the Wake County schools are (http://www.greatschools.org/north-carolina/raleigh/
It will be a huge task to view all those area you listed during the two days perhaps it would be best to narrow it down or even search some city data sites for some ideas of where to start. Cary will definitely give you the feel of Long Island with things in easy grasp and I know of quite a few apartment sites that have wonderful amenities and allow you to rent for shorter periods of time a good place to start when making a transition. Theres also a lovely complex in Brier Creek that just recently opened. The weather here is awesome (in case you haven't already realized that) :)
I would also encourage you to view my website to search further http://www.advantagecb.com/danderson.
And if you would like for me to have any of my recent clients reach out to you with their thoughts on where to start I am happy to do so. And of course if you have any questions feel free to call or text me 919-452-9379 or email me danderson @advantagecb.com.
Best of luck and welcome to lovely North Carolina!