What is the right folder to install .bin file

[Barry Yu <barryyupuilee sbcglobal net>]

As root, I downloaded the Audacity-1.2.xxxx.bz2 , and it is in  /root 
and I untar it, and then ./audacity-1.2.xxxxx.bin, and the installation 
goes on, created a subfolder /audacity-1.2.xxxxx under /root, I cd into 
it and ./audacity and the program starts fine.
I decide to install it out of /root so regular user can use it, /usr/bin 
or /usr/local which one should be the right place?, do I have to chmod 
a+x the audacityxxx.bin file before installing it in the new place?
p.s. : I am not asking for a yum install method instead of  the 
./audacity.bin because I had tried 2 repositories already but none of 
them worked, and the last resort is audacityxxxxxx.bin and it is working 
fine now)