Yes. Obviously the concept “go out for dinner” is a cultural one, but people did regularly leave their domiciles to purchase meals. An excellent example of this is Pompeii where homes didn’t have kitchens and there are dozens of bar like structures that people would come to in order to purchase their meals.

Remember that there were no microwaves. Cooking food was labor intensive and ovens and such required a lot of space and material to operate. Baking bread is hard even in modern times. It would have been nearly impossible for a city swelling Roman in such an environment to personally bake his own bread. However it should be noted that “meal” really means something like bread a drink and maybe nuts, meat, cheese, olives etc depending on how wealthy you were. There wasn’t a hell of a lot of variety.

Once again your question is super duper broad and covers a huge time frame, but yes people did do something analogyous to going out to eat.