The sentence reads ここにあるレストランはどれもおいしくない, and the translation given was "Any and all restaurants that are here are not tasty." When the word ある is used here, how is it able to modify restaurant so that it means "the restaurants that are here"? Is it just because of where it is placed in the sentence? Could this work with other verbs, like saying ここで食べる人 to mean "the people who eat here"?
Judging from your previous questions, perhaps this is the first time you learn about relative clauses. Once you know this keyword, you can find lots of good articles about this topic. Yes, ここにあるレストラン literally means "the restaurant(s) that exist(s) here". A more natural translation is simply "restaurants around here".
レストランがここにある。 Restaurants exist here.
ここにあるレストラン restaurants that exist here
As you have correctly guessed, ここで食べる人 means "the people who eat here".