I placed Neovim in usr/local/bin but getting permission denied I'm not sure where to place the Neovim folder (after extracting it). Is the location usr/local/bin correct?
I get the following
zsh: permission denied: nvim
The location of an executable is much less important for it to be run from Terminal than its permissions.

https://unix.stackexchange.com/questions/183994/understanding-unix-permissions-and-file-types/

Check them by running
ls -la /usr/local/bin/nvim


I'm not sure where to place the Neovim folder

You can place it anywhere you want as long as the shell can find it. Shell finds items using a variable named PATH.

https://en.wikipedia.org/wiki/PATH_(variable)#Unix_and_Unix-like
https://stackoverflow.com/questions/11530090/adding-a-new-entry-to-the-path-variable-in-zsh


Is the location [/]usr/local/bin correct?

It is correct only if this location is in PATH. Check it by running echo $PATH in your terminal. I personally like ~/Applications. If it is not in PATH: Open ~/.bash_profile/ ~/.zshenv in your text editor and add the following line to it
 PATH=&quot;/usr/local/bin&quot;:&quot;$PATH&quot;


ZSH: .zprofile, .zshrc, .zlogin - What goes where?


zsh: permission denied: nvim

You have two choices here:

Use Homebrew to install it and no longer worry about putting files in lib or share or bin folder.

Run
chmod u+x /usr/local/bin/nvim