So they have the basics...milk, little cartons of cereal, postcards, fruit and then other gift type items. T-shirts, hats, flip flops, I think I even saw umbrellas last time I was there. However, they are super pricey and definately NOT as cute as Disney items.
I'm not quite sure on what or who this basket is for but I would strongly suggest that you consider ordering from Vons (or stopping if you have a car). You can get fresh flowers, fruit, snacks, bakery items etc and right now delivery charges are free. If you wanted to add Disney items like tshirts, autograph books etc, then maybe a stop at Downtown Disney would be in order??
My other suggestion is that you can always mail or pack your gift/welcome basket with you. I always put together something special for DS from Mickey (of course!) and I will usually pack in my suitcase or mail it to the hotel ahead of time.
I've even ordered directly from the
DisneyStore and added on the gift wrap and a personal message (again from Mickey) and had it mailed to the hotel.