I just want a digital camera that takes quick pictures in low light when using a flash. Which camera is best?

Chek these out

http://tinyurl.com/udemp

They have some awesome ones.

There is only one compact digicam that has good low light performance- and that's the Fuji F30 (ok, and F20- same camera, a few less features).

Keep in mind that flash light that comes with almost all point and shoot camera are not very powerful. It will be okay for within 15-20 feet or so but the flash will not be effective for anything beyond that. I do agree with Morey000 on the cameras choice. They do very well under low light conditional. Even better if you set it on a tripod and NOT using the flash for night scene.

If your budget allow, you may want to consider the Canon PowerShot G7 and get yourself an external flash. This is one of the camera that you can attach an external flash on the camera. External Flash will greatly improve the range on how far you can shoot at night. Up to 100+ ft depends on which flash you get.