My concern is do I have to be there waiting to receive it or will the hotel sign for it and bring it to my room? We will be at GCH...does anyone know? Also we wouldn't have anything refrigerated....just diapers and baby food and snacks.
We've done this at GCH and at HoJo. You do not have to be there; the hotel will take delivery for you (although some people have called the grocery store in question and they said you had to be there-- but in my experience, the hotel just signs for you).
You try to time it around the time of your arrival-- tough to do, since the delivery window is 1-1/2 hours. If you are not there, the hotel will hold it for you at the bell desk until you check in.
Our experience: at GCH, our flight was late, so our groceries beat us. They held them at the bell desk; although they were not refrigerated, they were packed tightly in a cardboard box and all the cold stuff was still cold, no problems.
At HoJo, our flight was EARLY, so our room wasn't ready to check into yet at 2 p.m, and the groceries weren't there yet. They weren't that busy, so I asked them if, when the groceries came, they would mind taking them up to the room when it was ready and putting the cold stuff in the fridge for us. They did that with no problems, and the stuff was all safely put away in the fridge when we came back about 7 p.m. HoJo will NOT guarantee that they'll do this for you, but they will note your request, and in my experience, they bend over backward to make you happy. (Hmmm... not that I'm a HoJo fan, or anything.

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Does this save time and effort? Heck yeah! Do you really want to haul all the way down to Target for a rack of bottled water, take a taxi, figure out ART, whatever, so you can get some breakfast stuff and snacks for your room? Just have it delivered to your door! And don't pay $3 a bottle for a 20 oz bottle of water in the gift shop!
Just be sure and call your hotel before you go and let them know that you have groceries being delivered, and the time window.