We had lunch in a nice restaurant by the sea. This suggests there is more than one nice restaurant by the sea and you ate at one of them. We had lunch in the nice restaurant by the sea. This suggests there's only one nice restaurant and you ate at that one. Tim sat down on a chair near the door. There are several chairs near the door and Tim sat on one of them. Tim sat down on the chair nearest the door. There's only one chair that fits that description and Tim sat on it.

Note that the sentences about the restaurant the words "a" and "the" come before"nice", not after. "A nice restaurant" not "nice a restaurant".