Explorer toolbar button (or system tray icon) that moves current window to certain position?

There are tools that you can save preset locations on the screen and basically open them all at once in those locations. Optionally (what I prefer) is using Powertoys (fancy zones feature) which allows you to grid out your screen(s) how ever you want. Then you grab your program window, hold shift, and drop it in the grid you want

You can be a simple or complex with your zones like this