24/7 Customer Support. StorQuest Self Storage Madison is a seamless addition to your active lifestyle. Our brand new, state-of-the-art self storage facility is conveniently located on Shopko Drive near the University of Wisconsin and Madison College and close to East Washington Avenue and Packers Avenue, so it's easy to get in, out, and onto your next adventure. Stop by on your way out of town on a camping trip and pick up your tent and sleeping bags, or grab your ski gear as you head up to one of the area's local ski resorts.