Use Yelp to locate local food and restaurants. Put it in excel spreadsheets call them or email them to say u want to partner with them in promoting their services in return they share your site with their customers and give u a cut if they do get business from u.
Having business drive traffic to your site so their customer can get the coupon from your site. They only need to download your QR code or coupon code as they check out the restaurant.
The QR code will be given to those registered at your site and who visit the local store. This way you can retargeting those registered at your site.
And you may want to place ad on food blogger blog or u can create a food review blog featuring restaurants participating your coupons site and provide a link from your blog post to the coupon site.
Your food restaurant listings shall list the famous dish of the restaurant, current specials, maybe a bit history of the restaurant and what people has been saying about their restaurant and u rate each restaurant u provide coupon for.
You can pin photo of food on pinterest or Instagram and link back to your coupon site the specific restaurant of which the food u featured as pin was made from and they can register and get QR code immediately
Just a thought