The "out" does pretty much exactly what the Dictionary says. Namely it indicates that the evening at the restaurant was spent for purposes of pleasure or entertainment.

You can easily say we "Spent the evening at a restaurant," in the case where you work at the restaurant, or were there with a client on a harrowing meeting. But if you "Spent the evening out at a restaurant," the implication is you went with your wife and kids or friends, and the purpose was to enjoy yourself.

The "out" does pretty much exactly what the Dictionary says. Namely it indicates that the evening at the restaurant was spent for purposes of pleasure or entertainment.

You can easily say we "Spent the evening at a restaurant," in the case where you work at the restaurant, or were there with a client on a harrowing meeting. But if you "Spent the evening out at a restaurant," the implication is you went with your wife and kids or friends, and the purpose was to enjoy yourself. Edit: As User1 notes you can also spend the evening out at a restaurant alone, maybe treating yourself instead of having to cook. The essential point is that you go to the restaurant for purposes of pleasure or entertainment.