What does Google Sites do well? Google Sites provides a straightforward, free solution for building a basic site (with lots more opportunity to expand, host the page yourself, use your own domain, etc.). If you just need a simple personal or business site (e.g. for an academic or a small business), this is a nice choice to start.
What does Google Sites not do well? Like many new versions of Google services, it looks streamlined and simple, which can be nice, but some of the more powerful options can only be found by switching to the classic view. It's not super intuitive, but they do have pretty good documentation.
What do you wish you had known about Google Sites before using? I just wish I'd known about it earlier! If you do a little bit of research and work to get your site set up properly, this is a great solution for a basic web presence, especially if you don't need anything too fancy or self-hosted.
Have you used a competitor to Google Sites? If so, how does it compare? I've also used Wix some, but pretty quickly abandoned it because it was tough to use and had some fees I didn't feel like paying (since Google Sites is free).