24/7 Customer Support. Looking for somewhere to store your gear between life's big adventures? Check out StorQuest Self Storage in La Mesa, California. Located in the industrial zone near HWY 8 and the La Mesa Square Shopping Center, we make it easy for you to stop in, drop off, and hit the road. Whatever it is you need to store, from excess business inventory to surfboards and backpacks, StorQuest La Mesa has you covered.