As another poster said make sure your name and arrival date is on the shpping label somewhere. Call the hotel ahead of time and make sure they are aware a package is coming and see if there is another address they want used besides the mailing address of the hotel (sometimes they will have a different address for the receiving loading dock they will want used).
There have been a few times where I needed a box of books and/or a projector and didn't want to risk it not arriving with me and also didn't want to drag it from the airport to the hotel and have shipped them. I have never been charged a fee to receive them at a Hilton property but have been charged a fee at Hyatt's by their business centers before (I am a diamond at Hilton and was only gold or Platinum at Hyatt when receiving packages so not sure if status had anything to do with it or not).
Even as a diamond, the business centers have charged me a fee to ship the packages back to my house or office on top of the already inflated shipping prices. If you are shipping the stuff back home, I would see if there is a UPS store or other mailing facility near the hotel, it is cheaper to use them than the hotels business center.