The cost of renting a storage unit in Hampton 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 $$58 to $589 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.