Google maps the application might not be running, but it constantly runs a service in the background. Have a look at settings > applications > running services. You'll be able to stop google maps from there. It might keep the service running if you have options enabled like 'remind me to check in here' for latitude, which is still part of Google maps.
As for the screen, the only advice I can give is, turn the brightness down and make it time out quicker.