You MAY be able to deduct the mileage to and from your home to the storage unit IF you home is your "principal place of business (POB)".
To deduct mileage, the home just needs to be the "Principal Place of Business". It does not need to qualify for the Home Office deduction (the 'Regularly and Exclusively' rule does not apply).
https://www.irs.gov/pub/irs-drop/rr-99-7.pdf
https://www.irs.gov/publications/p463/ch04.html
https://www.irs.gov/pub/irs-pdf/p587.pdf (page 3) POB defined
