Where is the option for changing the style?
(Working from a 'yes')
Most sites it's either on the top right, bottom left, or bottom right corners.
Now, we're working from Joe Schmoe who hasn't logged in. Chances are he's not going to view the very bottom of the page, so that suggests upper right corner, perhaps on the same line as the main forum links.
For testing purposes, however, if we say that this is what such a feature would be used for, I would argue for placement in the bottom right corner, right under the PunBB copyright information.
Pull the currently installed styles into a dropdown (like how it's pulled on the Options page), have a 'preview'/'change'/'whatever' button, that refreshes the page with the new style. You could have this display or not based upon a prefence in the admin area.
The alternative would be to have a page/plugin on the admin side that allows you to do this. You would see a preview of the various pages, or various styles, and could preview stylesheets from there.
It removes this from the user's side, so they still have two/three clicks to preview a stylesheet (plus 2/3 more to go back), but it gives admins a useful tool at least ...