Burger pass. $30 for a burger pass. Gets you burgers for $4 for the rest of the year. or pay $20 for a burger now. You can secretly give out burger passes to locals when the tourists aren't looking.
Several of the local places do "frequent diner/visitor" loyalty cards, where the 5th or 9th meal (for restaurants), coffee (coffee shops), etc are free. This offsets the otherwise high prices charged on menu items.
Also, once a year (during the off season, of course), the local high school sells a booster card that gets a percent discount off for the entire year at numerous local places.
This is of course not unique to a touristy area, but I find myself using them far more often than in other places I've lived.
Any person travelling just coming by for the "best burger" probably would not want to spend $34 and not use that card anymore so $20 sounds great. Any regular would probably be super cool with paying that extra $30 knowing they can get a burger once a week or whatever for $4. This works out for the restaurant and the regulars, and like you said they can just hand out those cards to anyone for any reason.