"I eat inside the restaurant."
I'm afraid I don't understand. Why is the particle で used here, instead of the particle に? Do they not both indicate position (e.g. ...間にいます)? I've looked it up online, but I can't find a satisfactory explanation. Is this just one of those things that you need to memorize for every situation?
Basically, に is used for existance. That is, where something is located. で is used to denote where an action takes place. So, since we're describing where the act of eating is occurring, we use で.
の is a possessive particle, 中 is inside. レストランの中 can be thought of as "the restaurant's inside". You wouldn't use "the restaurant's inside" in English, but in Japanese, when you want to say you did something somewhere, you use で.
The same is with の隣(next to), の前(in front of), の後ろ(behind), etc.