"I go out to eat with my friends." should also work as a translation - nobody would say "I go to eat with my friends."
This is one of the instances where the present continuous tense works better than the simple present tense. "I am going to eat with my friends" vs. "I go to eat with my friends."
"Going out" implies leaving home to go to a restaurant, for example. this is simply eating.
Looking at the declension of "mein" can help. "mit meinEN Freunden" = "with my friends", "mit meinER Freundin" = "with my girlfriend"
and how to tell in german "with my girlfriends"? ;) "Mit meinen Freundinen"?
In most cases, the main verb takes the second position in the sentence and the rest of the verbs are at the end. Here 'gehen' is the main verb so it takes the second position. 'Essen' then, must go to the end.
"Dinner" is not specified anywhere in this sentence. It could be any meal or snack.