I was talking to my friend who isn't an English native speaker (A) and this is our conversation:
A: Do you want to go with me to an Italian restaurant?
B: Yes, where?
A: In the shopping mall.
B: I know which one!
My questions:
Your conversation is perfectly fine.
"Do you want to go to the Italian restaurant?"
This implies that there is only one Italian restaurant that the speaker could be referring to. The speaker is assuming that the listener knows that there is only one and does not need further clarification. Often, sentences like this are followed by qualifying prepositional phrases like so that the listener can determine which specific restaurant the speaker is referring to:
Do you want to go to the Italian restaurant in the mall." OR
Do you want to go to the Italian restaurant down the street.
"Do you want to go to an Italian restaurant?"
This implies that the speaker does not have a specific restaurant in mind, regardless of how many there actually may be (in fact, this sentence is acceptable to use even if there are no Italian restaurants).
So in summary, if there is one restaurant and both the speaker and listener know this, you should use Do you want to go to the Italian restaurant? In all other circumstances, you should use Do you want to go to an Italian restaurant?
In English, asking a question with the article a or an means the thing in that category in general:
1) Do you want to do go to an Italian restaurant [as opposed to a French or Spanish or whatever one]. Yes, I want to go to the one in the mall.
Another example:
2) Do you want a scone for tea? Yes, the green one. [on a plate]
Once the object or thing is identified, it would take the.
Do you want to go with me to an Italian restaurant in the shopping mall?
1) This would indicate many Italian restaurants in the shopping mall.
2) He is mentioning the restaurant for the first time.
Do you want to go with me to the Italian restaurant in the shopping mall?
And here the listener knows which restaurant you want to go to.
