Translation:We are at the restaurant by the beach.
In English, I think it is common to say that home, restaurants, etc are "ON the beach" especially if it is oceanfront property.
I think the distinction is really more "on the beach" implies it is right on the beach and "at the beach" can be the area around the beach but not exactly right at the border of the sandy part of the beach.
Exactly. On the beach would be "na plaży" whereas by the beach would be "przy plaży"
This is widely accepted, however, the precise terminology would be "by the beach" as restaurants are usually built on solid ground with plumbing and gas lines can be made available as well as the restaurants don't get flooded at high tide.
'At' or 'By' - the beach, would be the most accurate.
I think that schidzy and joleneybean are right about English usage. "On the beach" can also mean directly adjacent to the beach.
With regard to English usuage, it can depend on what part of the country or part of the town that you are from.
Not to be too nitpicky, but the types of beaches in Poland would definitely necessitate not building anything right on the sand! You can learn a LOT about a language by learning about the land it originated from.