Nikon P7700 OR Sony RX100
The RX100 seems a more capable camera, with
large aperture f1.8 at wide end (which I use a lot for family photos)
If the wide end and low light is important for you the LX7 might be worth a look. Probably worse high iso than RX100 but estimated similar like P7700 and LX7 has f 1.4 and equivalent of 24mm at the wide end...
the Nikon P7700 allows external flash.
I think bounced flash off the ceiling is so great
... and a hot shoe
I normally use a D300 and bought a LX7 yesterday - so I am biased