How to " Monkey Test" a website
Selenium allows you to search the DOM elements in a page, and simulate clicks or keyboard events directed to a certain DOM element. That's not quite the same as defining "non-clicking zones" (which would presumably be defined in terms of X/Y coordinates), but it might possibly be even easier this way.
I'd recommend gremlins.js, a "Monkey testing library for web apps and Node.js"
https://github.com/marmelab/gremlins.js
Disclaimer: we wrote it.