I don't wear a chefs coat to interviews unless it's soley a skills practical. I'd feel a little dorky. I'm of the school of thought that you don't wear your whites on the street. I wear a nice shirt over a white cotten undershirt(sometimes a tie, one of my mentors always arrived at work in a nice shirt and tie). I wear decent pants that can do duty in the kitchen.
I always have a clean (practically new) jacket and apron handy when I go to interviews along with my knife roll, just in case.
Hats...If you are a tall guy like me get yourself a nice black skullcap type hat. It looks professional and never out of place. I don't go for the do-rags or puffy hats. Not all chefs like the baseball cap. The tall paper hats SUCK since they fall apart unless you staple them, they always get knocked off by the air curtains and the vent hood.
For everyday kitchen use, I wear black drawstring pants I got from KingMenu, and online uni/restaurant supply company. Very good rates and long lasting pants. I tried the checks from Chefwear, but they were way too pricey and I wore holes in them after 6 months. I prefer black to checks since I can wear them on days off with out looking funny, and they hide stains way better then checks. I only got static about not wearing checks from an instructer at my culinary, never from a boss, but YMMV.
Shine your shoes too.