"I eat outside the restaurant."
The difference when で indicates a location, is that it indicates the location something takes place, where as に is used for the destination of a motion verb (when referring to a location using に).
レストランに行きました - She went to the restaurant. レストランで食べました - She ate at the restaurant.
The general rule is for verbs such as あります, います, 行きます, たちます, すわります, に is used for location. For verbs such as たべます, よみます, ききます, で is used, but they do often overlap each other in particular contexts.
の typically represents possession of something, for example 私の名前 is My name. It this context の is used for 'outside' as it belongs to the resturant in a way. It is the restaurant's outside area is a way to think about it I guess. I hope this helps and isn't too confusing
が often suggests a secondary topic in a sentence, however, you are the main topic in this sentence so you should instead use は. On top of this, the topic of a sentence is usually stated at the start of a sentence not at the end. So it should instead be 私はレストランの外で食べます。Although in this sentence it is implied that you are talking about yourself so there is no need to add 私は, leaving us with just レストランの外で食べます。 Hope this helps and isn't too confusing!