Without a linen closet in our apartment, we've thought a lot about where to store extra linens. We keep them in a large bottom drawer of the armoire in the bedroom. Four other ways you might store extra sheets and blankets:

1 In a blanket box. We like this one from Pompanoosuc Mills.
2 We love the planter at the foot of this bed storing extra blankets. Via Country Living.
3 in under bed bins, like these woven wood ones (used to be available at West Elm)
4 hang linens in your clothing closet on hangers like this one from The Container Store