The cost of renting a storage unit in Salt Lake City will depend on the size of the container that you prefer, your location and the length of the rental service. Storage units usually come in 3 common sizes. 7-foot storage units cost around $115 a month. They come with an initial delivery fee amounting to $80 up to $100. However, if the storage unit has to be shipped to your location, an additional $$45 to $453 will be added to your bill. All in all, renting a 7-foot storage unit can cost you around $380 to $400. Both 12-foot and 16-foot cost higher and can be rented at around $150 to $180 per month plus the delivery fee.