True story -- I was a first time mom, just back at work after maternity leave and had to take a 24 hours trip across the country. I was pumping while I was away from DD. At a major upscale hotel chain (that will remain nameless), they didn't have a fridge for me in my room, like they were supposed to, so they had me put my milk in their commercial fridge with all of their other food. In a split section decision, I didn't know what other option I had, so I went with it. When I got back from my trip, however, I ended up dumping that milk because I was freaked out about what could have happened while it was out of my sight.
That's a long way of saying -- you may find a hotel that will store it for you, but I doubt you would be comfortable with it; I certainly was not.