Hi, perhaps consider finding a digital PR expert who would be able to help you with this.
If you'd like to do it yourself, then setup accounts on Featured, Connectively, Qwoted and be on the lookout for any opportunities. Once you get enough coverage, start showing it on your site and setup a press page. When you've got a press page and enough instances of your client's name online (in various well known publications), this is when you can start pitching to local news stations and radio stations (and podcasts). This is my stage at this point. When people look for my brand name, the first thing they see if my website followed by pages and pages of newspapers and magazines with our brand name in there. This is what you'd ideally want.
So it depends on a few factors, how many pieces of coverage does your client have already, and how soon does he want to go on to these media placements. Ideally, it should be 3-4 months of reactive PR + then you start pitching because the moment he's on the news/radio, people will look him up and they need to be reassured that he's the real deal before thinking about going to his restaurant.
BTW, isn't tiktok/Instagram/GMB better for restaurant promotion?