Earlier I wrote about my new toy, Nook Simple Touch. Using the instruction at nookdevs (which was originally written for Nook Color, so I had to improvise a bit), I managed to tell Market and Google eBooks who I am and now I have both working.
There are screens in Market that I cannot read anything (e.g. application description); I am guessing either the application is trying to render the text in a color that is too faint on the grayscale display (unlikely but possible), or wants to use specific font not available on Nook, but haven't dug into the issue (yet).
A purchased Google eBook can be downloaded (on a PC) in the format that can be read on Nook via Adobe Digital Edition, so I have the same book readable in both Google eBooks application, and in the native Nook application. The formatting in Google eBooks for the particular book I tried was miserable (but that is the same as on my XOOM and not the fault of Nook Simple Touch device).