Build the web app portion that allows reservations to be made from the customers perspective, just like they have now. Integrate it with Twilio so that the restaurant receives an automated call and can confirm/deny the reservation on their end, without having to deal with a bunch of new hardware. You just tell them that they're going to receive a phone call with the reservation information and the options. There's little or no training required on their side, no additional hardware, minimal integration, no new systems. It's a more organic transition for a restaurant when you're trying to talk them into becoming a customer.
Innovating technology wise in the restaurant space is pretty tough cause sooner or later you're going to hit the wall of having to integrate with a dozen or more point of sale providers, no matter what you're trying to do (mobile/online ordering, reservation/waitlist systems, reporting systems, etc).
Oh, and because of their incredibly low profit margins, most restaurants can't afford to buy this type of tech. And the ones that do typically keep it for 5+ years between upgrades.
The worst part is dealing across vendors though. The APIs are incredibly inconsistent between them, and some are frankly, crippled.
solves the problem of having access to seating data and provides a compelling upgrade option compared to alternatives. hardware just needs to be a "dumb" Internet terminal (likely with a touch screen and print capabilities).
But there are a lot of issues. How do you confirm to the customer that their booking went through? What if no-one answers? The customer experience just isn't that great.