The Collaborative International Dictionary of English v.0.48:

Variety store \Variety store\
   a retail store selling a wide variety of items, especially of
   low price, as in a five and ten.
   [PJC]

Moby Thesaurus II by Grady Ward, 1.0:

31 Moby Thesaurus words for "variety store":
   boutique, chain store, co-op, concession, cooperative,
   countinghouse, country store, department store, dime store,
   discount house, discount store, emporium, establishment,
   five-and-ten, general store, house, magasin, mail-order house,
   market, mart, post, retail store, salon, shop, store, supermarket,
   trading post, variety shop, warehouse, wareroom, wholesale house