Parallel install for testing?

I want to make some major changes to the CSS that controls my page, and am comfortable backing up and reversing changes. But, in case of major breakage – but where I know tweaks can be made to repair – I’m wondering whether I need to install WP again in a separate directory and use that just for testing, so that when it is perfect, I can move over the necessary alterations.
It’s not that my page gets a huge number of hits, it’s just that like anyone, if there is going to be a change, I’d like it to be smooth to the viewer, and for my trial and error process to be between me and my monitor 🙂
So is doing a parallel install the way to go on this, or is there any easier way maybe just involving the copying and renaming of a couple of the wp files in the directory that I currently have ?