If you need all things you said above and you can pay slightly more than 500$ I'd recomend you to buy a Panasonic Lumix DMC-LX100. It's 569$ on amazon right now. It has a hotshoe mount, best in class sensor with 12.8mpix and an insane low light performance, EVF( Electronic view finder ), a small and good looking body, it is capable of 4k video and has a 24-75mm f1.7-f2.8 lens. It's also equipped with wifi and NFC.
If size matters more than a hotshoe for you, then you should get yourself a Canon PowerShot G9 X Mark II. It's 449$ and with its size of only 2.3 x 3.9 x 1.2 inches ultra portable. It features a large 1inch sensor, a 3inch touch display, 1080p video, canons newest image processor, wifi, NFC and Bluotooth build in and can be controlled with your smartphone.
If you are really into premium desing, the Canon PowerShot G5 X is the camera to go for. With a 1inch 20mpix sensor, a hotshoe mount, an EVF, a really good autofocus system and a zoom range of 24-100mm at f1.8-2.8 it's a great camera. But as canons top of the line point and shoot it's price of 729$ isn't cheap at all.
Panasonic Lumix DMC-LX100: https://www.amazon.com/Panasonic-DMC-LX100-Digital-3-0-Inch-Vario-Summilux/dp/B00O2TI1GU/ref=pd_rhf_dp_p_img_11?_encoding=UTF8&refRID=QP8YSCWNV2ATAQMWEFWC&th=1
Canon PowerShot G9 X Mark 2: https://www.amazon.com/Canon-PowerShot-Digital-Camera-Bluetooth/dp/B01MT3SZ46/ref=sr_1_1?ie=UTF8&qid=1501093003&sr=8-1&keywords=g9x
Canon PowerShot G5 X: https://www.amazon.com/Canon-PowerShot-Digital-Camera-Optical/dp/B0167Q0VP4/ref=sr_1_1?s=electronics&ie=UTF8&qid=1501092913&sr=1-1&keywords=gx5
I hope this helps you to decide what camara you get.