You're going about this wrong and a lot of the advice here is also wrong, by worrying about the consumer experience first. Stop what you're doing and get out and talk to restaurants.

Make sure that restaurants are willing to offer rewards, and get signed commitments from at least 10 restaurants that they will do so, based on the metrics that they define matters.

Next, use the restaurants' existing social media outlets to get their own fans signed-up into private beta as an "exclusive privilege" to their fans.

If you can't get restaurants to do those two things at this point, you have a high likelihood of failure should you pursue development of an app without this important piece of customer development complete.

Happy to talk to you in a quick call to provide more details about what I'm describing above.