If you mean the restaurant when she was on her first 'date' with Edward. They went to an Italian restaurant called Bella Italia and she had Mushroom ravioli.
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Bella asks him if he could eat human food - and he said 'you can eat dirt, right?' and h does then
The answer is, Mike thinks that Edward wants to eat Bella.
Bella's baby (Renesmee) does not actually eat Bella. The 'health issues' that came with Bella's pregnancy were mostly related to her bones and energy. As Renesmee got physically bigger, she actually cracked one of Bella's ribs. What causes Bella to have to deliver is when Renesmee accidentally breaks Bella's back. Renesmee is/was incompatible for Bella's body, according to Carlisle's diagnosis in the books. Renesmee wanted to drink blood (she was "thirsty"), and she would get nourishment from the blood, yet Bella had not been drinking blood at the start of her pregnancy. Because Bella wasn't drinking blood, the baby wasn't nourished, and so womanly things happened (rough translation), and she didn't handle the early stages of her pregnancy well.
The name of the diner is " Frosty Palace ".
"The Martian Boogie" by Brownsville Station