You didn't mention whether you were staying in a studio or the 1 or 2 bedroom units. The studio has a small sink, a microwave, and a small fridge. They have paper plates, cups, and plastic utensils. They also have dish soap and plenty of hand and body soap for 4 days and more. The 1 and 2 bedroom units have a full kitchen with real plates, glasses, pans, both eating and cooking utensils. They also have dish soup and plenty of hand and body soap. Also both kinds of units have plenty of paper towels. They also all have hair dryers in the bathrooms. Only the 1 and 2 bedroom units have washers and dryers in the unit. If you're staying in a studio, you can get tokens at the front desk to use the washers and dryers in the hotel. This is only for DVC guests. Hotel guests have to pay to use the washers and dryers.
Really the units are well stocked. If you're after easy to get groceries you can go to White Water Rapids, which has groceries but also serves fast food. If you are staying long enough to order a lot of groceries you can either order directly though the Grand Floridian hotel or have Ralphs deliver, but you have to have a minimum order.
Hope you have a great time. What I like about the Grand Californian is that you are so close so both DCA and DL. Ride Grizzly River Rapids, get soaked, and you're back in your room in 5 minutes to change and throw all the wet clothes in the dryer!