If your restaurant website is not friendly to mobile visitors, search engines are going to penalize it. Your website will not appear early in search results if it provides a bad experience to mobile visitors. Simply put: less visibility in search means fewer people finding your website, and fewer people through the front door of your restaurant.
Just run it through Google's Mobile-Friendly Test page - and voila!
Google's study on local search behavior highlighted the importance of presenting a mobile-friendly website specifically for people looking to find local restaurants and businesses.
Your mobile website is not just a necessity for functional business reasons - it's a reflection of your brand. Increasingly, it is a measure of social proof. 57% of users say they won't recommend a business with a poorly designed mobile site.