It depends a great deal on what you enjoy doing, and of course the weather. If you want to do Splash Mountain (it's awesome!), you may get some wet shoes. No one likes walking around all day in wet shoes. Teva Sandals are the overall favorite, because they have the soles comparable to a really good tennis shoe, yet are designed to get wet and dry out quickly. There are various models of Teva's, so depending on what you like, and how much you want to spend, you may want to look at a variety of styles.
If you prefer the non-water type rides, and the weather is warm, look for a shoe that breathes well, (Florida is really warm and humid), and has a comfortable sole. You will be walking on hot Asphalt and sidewalks all day. You will need to wear something. If it's a cool day, your Nikes will be just fine. If it's a hot day, you will cook your little piggies.
Hope this helps. Oh, and one last word of advice, the cheapest Teva's are not always the best one's. The secret is in the sole. The cheap Teva's have a solid sole, the more expensive one's have a sole made of several types of materials. I've also heard good things about 'Sandals' brand as well.
All play and no work, makes me a happy boy.