NOTE: you will be prompted to log in to your Google account when you access the above link. Please review the Frequently Asked Questions about removing your data from Google.
Google Sites are currently not included in Google Takeout, but there is a import/export tool that can be used to extract a Google web site along with all attached images, videos, pages, etc.: https://code.google.com/p/google-sites-liberation/.
Download the import/export tool. It will run directly from your computer's desktop (Windows or Mac). Here is an example of the information you will need to enter in the import/export tool: