The rule of thirds does generally produce a more interesting picture. Obviously it's not absolute nor should it be adhered to religiously, but it is a good guideline.

Anyway, to adress the original topic rather than indulge in a debate of photographic theory with a bunch of amateurs, I now digress (or perhaps regress). :fawk:

One other setting you should take into account for good night shots is the ISO, or light sensitivity of the camera's image sensor. Go into the menu and see what it's set at. On automatic, the camera will tend to use a more sensitive setting in low light which produces image noise that you don't want. Since in low light you're going to be using long exposures no matter what, you want to set it to the lowest (i.e. least sensitive) ISO setting which will reduce the amount of noise the camera puts into the picture. This is especially important because noise due to ISO setting is most noticeable in low light situations and pictures with lots of dark areas in them.

Anyway, my elitist/purist/snob recommendation is that you can only learn so much with a point-n-shoot digital camera. You'll be way better off learning how to take pictures in black and white with an old school fully manual 35 mm SLR. Back in the day manual features that were controlled by actual mechanisms were the norm and automatic stuff was considered a luxury feature. Now adding a manual function to a fully automated software-controlled gizmo is a luxury feature.