For both cases I strongly recommend looking for something with

• a fast lens (A 2.0 aperture 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 2012, both the Canon S110 and the Lumix LX7 offered that set of characteristics. If you don't mind a slight bulkier camera, you could also consider the Canon G15 due to its movable LCD.

And last but not least, if you can afford the extra cost, the Sony NEX (the NEX 5N for example) and the micro four thirds offers from Panasonic (such as the GF5 and GX1) and Olympus (such as the E-PM2 and E-PL5) 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 and the Nikon 1 cameras.

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).