Slow down NginX
I don't see why it would, /var/www is exactly where I would put it.
Accessible to other users.
By default /var/www should be owned by root, with read and execute permissions for the webserver user and read permissions for other users (so that you can log in and look at the files without having sudo). If you want to be extra secure, change the group ownership to www-data (or whatever your nginx user is on that machine), then set
root rwx
www-data (group) r-w
all ---