MacOS – Adobe Illustrator alternative for the Mac

You could follow the instructions on this page at Adobe and uninstall the CS5 packages you don't need.

If you want to get rid of even more useless space, you could try Monolingual, which removes unneeded language resources.

After checking the system requirements on the Adobe web site I could say: No, you can´t use Adobe CS6 Illustrator with your Mac because of the lack of RAM (1GB instead of 2GB) and no 64bit processor as Apple said it on your support document.