Is there a way to tell Windows on which monitor it should open a windows independently of where it was closed?
Windows 7 does not have a specific user setting to tell a program where it should open, so the first time you run a program it will open the program main window in the primary monitor. However, Windows 7 will remember the monitor where your applications were last run, so once you've opened the app for the first time just move the main window to the desired monitor and close the app: the next time you run it, it should open in the same monitor.
You can also use the combination of [Windows Key] + [Left/Right Arrow Keys] in order to fast move the active window between monitors.
Apart from that, you can use a third-party app to do so. To start with, several video driver applications like ATI Catalyst or nVidia Desktop Manager are able to manage where the window of a program is opened. You may also want to test utilities like MaxTo or Display Fusion.