I am not familiar with your model, but if it has manual modes, you will get better results using them. It is important to get a longer shutter speed in order to collect enough light. This introduces two potential problems though. With longer shutter speeds, camera shake makes blurry pics. A tripod is needed to correct this. It also helps to set a delay of a couple seconds to prevent shake from pressing the shutter button. Most cameras have this delay feature of between 2-10 seconds. The other problem is that with long shutter speeds anything moving in the image will be blurry. If it is night portraits that you are after, see if your camera has a special mode for it. If not, set the shutter for long enough to properly expose the background, use a flash to properly expose the people, use a tripod, and have the subjects keep from moving until after the shot is complete. People have a tendency to think the shot is over once the flash has gone off, but with a night portrait this will cause a blurry trail. If it does have this mode, it will do these things for you. It might also help to set the ISO to a higher setting, but be aware that this also adds noise.
The best thing to do is play around at home before your vacation and make note of what settings worked the best. When practicing, take it all the way through to how you expect to use the vacation pictures. For example, if you plan on printing the vacation pics, print the tests to make sure they look good. Sometimes images look decent on screen but not when printed.
To get the best night shots, you really need a DSLR with a good lens. They have less noise, so high ISO settings do not ruin the image. In case you do not understand ISO, it is sensitivity. A larger number means that less light is needed to capture the image. But as I said before, it does add noise. On some cameras, the highest ISO makes the image practically unusable. For the lens, a good prime one (i.e. no zoom) with a usable large aperture would probably be the best. If you use too large of an aperture though, the background will go out of focus. This is often desired, but maybe not in a night shot. It comes down to your preference. If you decide to spend the money and go this route, read up on the camera and lens reviews before you buy to make sure you get what you want. Pentax makes a less expensive DSLR that is still very nice, but Canon and Nikon offer fairly inexpensive, but good prime lenses. These are the top three brands for DSLRs in my opinion. I have heard that the ISO noise in Olympus makes it not the best for low light shots. I am not familiar with the new Sony ones, but they look interesting.
Good luck!
Kevin