For something a little later in the afternoon, and a little pricier, try the tea. It's served in the pretty little lounge off the main lobby, overlooking the pool.
You can chow down on itsy bitsy tea sandwiches and scones, and really get filled up easily.
They serve a zillion different types of tea, as well as coffee. I believe they start serving tea around two.
It's something altogether different, and unique to the Grand Floridian.