Whether your move to an apartment is temporary or you have sentimental belongings you aren't able to part with, there are a couple of different apartment storage options you can look into. Private Garages: Apartment garages may be attached to your apartment and included in your monthly rent or detached and rented separately. Exterior Storage: Some apartments have exterior storage closets that are accessed from your patio, while others may offer storage closets in the breezeway that can be rented for an additional fee.