I don't know that I have any crazy "out of the box" ideas for you aside of maybe recommending a bounce house out front (those things are awesome).
But seriously, I have one word for you: Trip Wire.
You need something to get people in the door for the first time. There's something very powerful about someone converting into a customer, even if they only pay you $1.
If you price your sales funnel correctly by having easy up-sell items and profit maximizers (think: Soda, beer, fries, etc) then you can actually sell your "trip-wire" at cost or even lose money on it.
If you choose to use a "coupon" to advertise your trip-wire, make it a specific dollar amount and not a certain percentage off. "$.50 cheeseburgers for this week only" instead of "30% off this week". Don't be afraid to make it crazy. You have a lot of competition.
Then, as long as the quality of your establishment is high, you will certainly enjoy a consistent stream of repeat customers following your tripwire sale.
I would also add that some serious follow-up needs to be involved to ensure LTV of a customer is high. Make sure you have an email list - maybe even have them exchange their email to receive the tripwire deal.
Once you get a funnel like that lined up (and this works in ALL businesses), you can spend more to acquire a customer than your competition, because you'll make it all up on the backend. That's a pretty powerful situation, as Amazon can attest to.
Let me know if you have any questions! Shoot me a reply on Clarity.