The usual place to install things that you want to be generally available on your own system is in /usr/local/include.
Code:
$ echo | gcc -xc -E -v -
...
#include "..." search starts here:
#include <...> search starts here:
/usr/lib/gcc/x86_64-linux-gnu/5/include
/usr/local/include
/usr/lib/gcc/x86_64-linux-gnu/5/include-fixed
/usr/include/x86_64-linux-gnu
/usr/include
End of search list.
# 1 "<stdin>"
# 1 "<built-in>"
# 1 "<command-line>"
# 1 "/usr/include/stdc-predef.h" 1 3 4
# 1 "<command-line>" 2
# 1 "<stdin>"
Of course, there is also the option of putting various -I/path/to/here options on the command line whenever you want to compile with one of your own libs.