What is a another name for restaurant or cafe that only serves appetizers?

Answer 1

Restaurants like this of the spanish/carribean nature are called a Tapas Bar. Many other nationalities are claiming they are "Tapas Bars" as well.
Other than that small dishes are generally served at Cafes as well as alcoholic drinks and small dishes at most Lounges.

Hope this helps.

Answer 2

Look for places that serve Tapas (Spain). They are small portions of food which are served as part of the social scene.