Old Sites and New Sites--Like Night and Day
Google Sites has power as a teaching and curation tool for students to show what they have learned, or for you to manage your learning environment. If you're looking for just a management tool, Google Classroom is your answer--not Google Sites. However, if you want to get students involved in creation, Google Sites can get it done. Be sure to play around with it to see all the quirks, especially if you're using the "old" side. Some of the things you'll need are buried within strange places in the interface.
How I Use It
OLD SITES...I used the "old" Google Sites as a teacher page, and I also created an ePorfolio template through our domain to have students digitally warehouse the information they learned in my class. It takes a lot of time to setup these templates to your satisfaction, and students will struggle with the edit interface. In a 1:1 Chromebook environment, the interface to Drive works well, but be prepared to spend a lot of time working with students individually.
NEW SITES: It's much easier to design "new" Google Sites, and they are significantly more visually appealing than the "old" version (think Weebly-esque). However, there's no ability to create and share templates, meaning that if you want to do the ePorfolio route with students, be prepared to do a direct instruction piece with students on devices. The "drag and drop" interface does work well to pull resources straight from drive, and the image search allows you to find royalty-free images to place on your site to add some aesthetics.