convenience store

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A small retail store that is open long hours and that typically sells staple groceries, snacks, and beverages.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A small retail store, often in a residential area, that carries a limited selection of items such as staples, junk food, and drugstore items, and which is open long hours for the convenience of shoppers.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a store selling a limited variety of food and pharmaceutical items; open long hours for the convenience of customers