Use the adjective fusty to describe something that's covered with dust and smells a little old and musty. Your grandmother's attic is probably full of fusty knickknacks.
Fusty is perfect for describing anything from a slightly mildewed quilt at the back of your closet to your brother's camping gear, forgotten in the trunk of his car for months and smelling a little ripe. You can also use it to talk about an antique idea or attitude, like your uncle's fusty, outdated opinions on the roles of men and women. The Old French root of fusty is fusté, "tasting or smelling of the cask," from fuist, "wine cask."