Hola Paul

It wouldn't be wrong to use the article "que nos den un asiento en una mesa..." but we drop it because we are using the word "asiento" with a very general meaning, as in "any seat"; it's also pretty much a set expression used without the article, for example, you could hear from the waiter as you enter a restaurant something like "tomen asiento por favor" (no article here either), meaning "please, seat/take a seat".

Another similar example where we drop the article could be for example:

We are thinking about coffee in general, not a specific coffee.

Saludos

Inma