I recently built an app that includes the option for downloading to the Apple iOS store, Google Play store - or you could just click to open it up in your browser and call it a day.
I looked and couldn't find a nice logo to put next to the other two, so I made one. It's not fancy, but I particularly like the way that the Open Web App text covers both the action for an end user (click to open) and also subtly reinforces the idea of an open web.
I did find a few logos for PWAs, but IMHO I rarely encounter an end user that knows what in the world a PWA is. Just calling it a web app seems more reasonable. Offline mode for most users is just a feature of a web app.
The font is just Open Sans.
You can download it in a variety of formats. Released with a MIT license. Go nuts.