Display usually does soak up battery - but for the usage you are talking about it sounds like some app is waking up the phone frequently through the night. If you tap on the battery graph one more time it should show you periods for Awake, and Screen On. Try to get familiar with the list in settings, applications, running services. I have a few I'm on the look out for, eg. bad programming some of these are on when they should really turn themselves off such as the one I have SugarSync. It tried to synch to the cloud even though I tell it to only when I have wifi connected. So sometimes I kill the service to make sure it does not suck the battery. (admittedly they seemed to have improved with recent updates).
Anyway there are plenty of sloppy programs that do this. Also look out for the crapware that the cell network providers put on there - they are not known for their efficiency. It's not the SGS2 per say , just the stuff loaded on it. Search around the forums knowledge is the key. Now my overnight discharge is more like 5%