What digital cameras are good with low-light and...

If the low light shots are of building or such, you can put any camera on a tripod. If you need to do them hand held (street photography/ concerts/ sports/ etc.), you're out of luck. This is the domain of digital SLR cameras. The digital Nikons are good at this, and the Canons are even better. They can go up to ISO 6400 in a pinch, and they'll deliver beutifull image quality as high as ISO 1600. This is better than film ever was. If you add a light sensitive lens, like a 50mm f/1.4, you can do action photography by candle light. No compact camera comes anywhere close to that. (The autofocus will hunt forever, and when it does lock on, you'll need a shutter time of several seconds.)
If it must be a compact, get one where you can crank the ISO up to 1600 (or higher).
For extreme close ups, get a macro lens (or a compact that has a macro function.)