We have been designing many Google Sites these past few months. Kirksville Web Design has a new initiative to always use the responsive web design feature of Google Sites, known as the "Automatically adjust to Mobile" feature. This results in a few design limitations, but a lot of benefits for web property owners, including SEO page rank points.
As you may know, you have two backgrounds to play with in Google Sites: 1) Background Image and 2) Background Wrapper Image. The wrapper image has a higher z-index, meaning it is layer on top of the background image. You also have background color at your disposal.
We've been designing for a lot of schools lately, which is wonderful. We have a bunch of samples here in this Google Doc. All Google Sites.