Do You Need Storage? Come to the Storage Cave.The Storage Cave is a locally owned and professionally managed self-storage rental facility serving Omaha for almost 30 years. Their units are clean, secure and perfect for home and business storage. 24/7 Security Small, Medium, Large Units Conveniently Located Short-term & Long-term Options Drive-up Access Gate Access 7 Days per Week With a great central location at 80th and L, you can get here from almost anywhere in the greater Omaha area in about 20 minutes!