I think someone can either say 'I don't want to split up' or 'I don't want to eat there', but not both. If someone's going to absolutely refuse to go somewhere ever, be it Local Place or McDonald's, they can't also specify 'don't leave me'. If neither party wants to split up, then the only option seems to be, they both go to the place the other wants and perhaps have a drink while their friend eats.
Splitting who chooses the restaurants might work for some people, but not always, if there is one or more parties who won't/can't eat at some places. I would be really unhappy giving up half my dinners to eat at a fast food place while on vacation, and equally someone who doesn't want to eat non-Western food isn't going to be very happy to get dragged to local places half the time.