Where should I put my script?

A Google search for "Linux file system hierarchy" will turn up several documents, including this one.

Where you put your script depends on who the intended user is. If it is just you, put it in ~/bin and make sure ~/bin is in your PATH. If any user on the system should be able to run the script, put it in /usr/local/bin.

Don't put scripts you write yourself in /bin or /usr/bin. Those directories are intended for programs managed by the operating system.