If you know me, you'll know that I routinely use private browsing all the time. I don't care to have the browser remember any of my personal data or what sites I've visited. If I really wanted to remember something, then I will bookmark or blog the page. This means that when I use Google Chrome, I'm using its Incognito mode all the time.
One drawback to Incognito is that it also doesn't remember the screen location of the last window you used. In other words, I want the Incognito Chrome window to open in the same place on my screen every time I open a new window. This is actually a good feature because Incognito's purpose is to remember NOTHING. This should also include locally stored settings like screen location.
To get the window to open in the same place, just open a normal Chrome window, move it to the place you want it, close that normal window. Next time an Incognito window is opened, it should open in the last location where the normal window was closed.
Happy Computing.