If the vendors were a post type and the food and the location was a taxonomy, this would be very simple. Taxonomies are used to categorize post types. Usually it is the best to have the main item (in your case the vendors) as post types, because you want those as results, and you want to categorize them (using location and foods types).
Currently the vendors are taxonomy terms, which can be assigned to the foods (products, which is a post type). This setup is great for shops, where multiple vendors sell the same products, and the user needs the ability to choose which vendor he wants to buy the product from. However it is not possible to use the product as the filter criteria to list the vendor with this setup.
I am not sure if there is any search/filter plugin out there capable of filtering taxonomy terms by assigned post types, it is used the other way around.