Usually when talking about "point and shoot" cameras people mean fixed lens compact cameras. The cameras we are discussing have detachable lenses but you can use them to "point and shoot".
If you can find a Sony Nex-3N for US$330 that's great but I doubt you will. The Nex-3N is portable and has high image quality. You might find a Nex-5R (the next model up) for around $350 as it has been discontinued - it focuses slightly quicker and has a touchscreen like the EOS-M but like the EOS-M its flash is an external unit.
The EOS-M doesn't focus very quickly although it's much improved after a firmware update. Unlike the 3N its kit zoom lens doesn't collapse but the 18-55mm lens the 5R usually comes with in the US doesn't either.
Another option you may consider are the Nikon 1 cameras like the Nikon S1 and Nikon J2. The two are very similar except the S1 is slightly smaller and lighter and has a lower resolution screen. The Nikon J1 is nearly the same as the J2 except it has the same screen as the S1. They all focus
very quickly in reasonable light.
A second hand J1 with 10-30mm lens is under US$200, a new J2 with 11-27.5mm lens is US$270, a new S1 with 11-27.5mm lens is $289 and a new J2 with 10-30mm is a little over US$300.
The 11-27.5mm lens is 1.1cm thinner than the 10-30mm but lacks image stabilisation. The S1 with 10-30mm lens option may be unavailable in North America.
