$1 First Month's Rent - Please visit the website to view In-Person Assistance Hours. Are you looking for the best storage units in San Antonio? Find them at 20523 Stone Oak Pkwy ! Store Space offers premium features and amenities at the lowest rates, so you get the best storage experience! Store Space Stone Oak in San Antonio is just west of US-281, convenient for those in the Stone Oak neighborhood as well as Timberwood Park, Hollywood Park and Roseheart. You can choose how to rent with us at Store Space. Just call, click or visit our store! Give us a call or make a reservation online to complete a Touchless Rental. You can also use our self-service kiosk in-store or find a unit with the help of our storage professionals.