For both cases I strongly recommend looking for something with
- a fast lens (2.0 is faster than 2.8 for example)
- reasonable ISO handling (at least 400, but preferably 800)
- the biggest sensor available
The sum of these factors are really critical for low light situations.
In 2011, both the Canon S100 and the Lumix LX5 offered that set of characteristics. If you don't mind a slight bulkier camera, you could also consider the Canon G12 due to its movable LCD.
And last but not least, if you can afford the extra cost, the Sony NEX and the micro four thirds offers from Panasonic (GF3 and soon the GX1) and Olympus (E-PL3) are certainly better than the previous options and offer the flexibility of interchangeable lenses. A middle ground, offering interchangeable lenses but a smaller sensor, would include the Pentax Q.
Note that these are current examples, but the market is always offering new cameras. The important thing to keep in mind is the sum of the above mentioned factors (fast lens, ISO handling and sensor size).