Colours define the type of customer who a restaurant will appeal to. They define the emotions that the design has to convey and they start the conversation with the customer. Before they've even read the name on the sign over the door people have understood what its colours say.
Colours can set the design apart from competitors (or make it fit in) and they can act as a visual shortcut to instant brand recognition. This is why big brands select very precise colour schemes and stick to them.
Colour selection is often not given the professional attention it deserves. I like to select colours very early on in the design of a restaurant before pretty much all the other work and as soon as I've clarified my client's instructions, researched competitors and defined the target.
Non-designers nearly always get this wrong. To tell the truth so do many paid designers. Mostly because they choose the colours they like personally.
I always employ a trained Colour Psychologist even on the simplest projects. It makes a huge difference to the outcome and potentially to the success of the whole venture.
By way of example here's a colour palette I just produced with my team for a small Indian restaurant. (I'd publish something for a bigger project but it wouldn't fit.)