Looking on the internet deeply has found these results:

go out to eat is the most popular phrase on the web.

go out for diner 1164,000 results on the web	go out to eat 115,900,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	I decided to go out to eat. On second thought, let's go out to eat. On second thought, let's go out to eat. We love our neighborhood, but sometimes the last thing you want to do after fighting traffic is get back in the car to go out to eat. I heard they go out to eat together... Would you like to go out to eat sushi together? At the end of the day, he'd want to go out to eat or dance, but I was always tired. You get a paycheck, but they also give you an allotment of money that you can use to go out to eat, or grab cigarettes while you're on the movie.

go out for diner

1164,000 results on the web

go out to eat

115,900,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

I decided to go out to eat.
On second thought, let's go out to eat.
On second thought, let's go out to eat.
We love our neighborhood, but sometimes the last thing you want to do after fighting traffic is get back in the car to go out to eat.
I heard they go out to eat together...
Would you like to go out to eat sushi together?
At the end of the day, he'd want to go out to eat or dance, but I was always tired.
You get a paycheck, but they also give you an allotment of money that you can use to go out to eat, or grab cigarettes while you're on the movie.