A few months back, we were approached by a bar owner who was interested in outsourcing his foodservice. This particular barman was well versed in the bar business, but had no interest in food. He had purchased an existing sports bar that offered basic "bar food". He wanted to upgrade their food offerings, but at minimal effort on his own part. It seems to me that there may be other bars in this situation. Really, any business that offers foodservice without that being their core business might be interested. Bars, bowling alleys, sports arenas come to mind. Sort of a contract foodservice deal.
There are a couple of reasons that I think this approach might work better than marketing to existing restaurants. I tend to think that usually, the restaurants know their menu, know their clientel, and much of the time, would rather develop menu items in house if they think they will sell. Of course, there may be exceptions to this, but they would be just that, exceptions. Also, restaurants will be less likely to promote your product with your name on it. To grow your business you will need to build your "brand". While that sounds like marketing gobbledygook, a brand is nothing more than a name that people identify products or services with. While a non-typical foodservice location may be more willing to promote "Blazing's Famous Burnt Ends", allowing you to build business through word of mouth or otherwise, a restaurant is more likely to promote "Our Secret Recipe Famous Burnt Ends". You catch my drift.
As for our operation, the deal between the bar owner and us didn't work out, as it didn't really fit in with our core business. I still see an opportunity in that market for someone wanting to get started in the business. As for how to approach any business that you would like to market to, I'd suggest showing up, asking for the owner, and have a chat with them. Some samples of your food would also most definately be in order. Good luck to ya, and hope it does well for you!