Raising prices sounds like the best strategy. You keep raising until the workload returns to normal. If you feel you're serving the wrong customers, you now have time to figure out how to fix that. Otherwise, if people eventually get turned off by the price and your workload goes down, you drop the price, and keep dropping it until you reach a stable point with just the right amount of orders.
And as the original commenter noted, you could put coupons in the local newspaper and the library and whatever else, so the locals have access to burgers at the old price.
Ask any family restaurant/bar owner in a seasonal tourist destination and they’ll explain why locals must be one of the first considerations before you make drastic changes. Particularly if an important reason for opening was a personal preference to serve locals over tourists in the first place.
It’s incredibly interesting to see how few people understand that someone may open a business with priorities other than massive growth potential.
It really is interesting, but hardly surprising, given the demographics of this forum. :)