Big Red Shipping and Storage is a student run business in collegetown. It has grown tremendously in the past few years as a result of Cornell eliminating storage space for students in the dorms. Big Red Storage has a contract with Cornell and heavily advertises to students.
For students who live far away or those who don't want to lug their stuff back and forth between college and home, this is a very good option. The biggest advantage is that Big Red will send people to your apartment or dorm room to pick up the boxes of stuff you want to store. For those without a car, this is a huge benefit. In fact, even for those with a car, it saves the time and energy of having to carry heavy boxes to a storage facility.
Many of my friends have used their services and all have come away happy. The rates are competitive and the non-monetary benefits really make this one of the best options for storage in Ithaca.
For Cornell students looking to store your stuff, this is a good option and I would recommend at least putting them on your short list.