Super-minimal version approach:
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On page load, get the location of the user (latitude + longitude) using HTML5 geolocation. This is done using Javascript, as in this example: http://www.w3schools.com/html/html5_geolocation.asp
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Show user a simple form with just a text box and button ("Search"). Then, the user enters the name of the restaurant they're looking for into the box and clicks the button.
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The form submits the user's text as well as the latitude/longitude from step 1 (as hidden fields in a POST request), this goes to a URL you've coded on the backend.
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On the backend, the web app feeds the text and lat/long into a Yelp API search ( http://www.yelp.com/developers/documentation/v2/search_api#searchGC ) and then grabs the first result, and shows it to the user with whether "accepts credit cards" is true or false [see note below.]