Rent a car, you will miss a lot without one. Also, if you're kiting you will likely want mobility to hit Barkers in the NW, East End to the east and Rum Point to the NE depending on wind and other considerations. Plus it is a good island to drive around to see sights, grab lunch, dinner, etc.. There is a map of some spots I put together sometime back at: http://tinyurl.com/y883bor
Just make sure your mind is well programmed for driving on the left side of the road. Round abouts are some of the trickier things for USA drivers to get used to. You can find some rentals on Expedia.com, just make sure they are open when your flight arrives. There are local companies too, usually at competitive rates with what you might find online. Don't recall anything other than having to show a valid US drivers license.
Or, you can take a just hang out at Compass Point for most of the time. Mike will take you out by boat to some areas you may not want to kite to. Plus they have a new operation near Rum Point you can probably get a ride to from shore. Say out to the reef for some waves.
As to all the misc. charges, you've got me. Whatever it is, not excessive as I recall it, Cayman is worth it in my opinion. You might find answers to that stuff on google.com.