First off, I would definitely recommend renting a car to get between Muscat and Abu Dhabi. You can't get to know the people and culture at 30,000 feet. You need your feet on the street. Muscat should take up a few days and there are interesting sights between there and Dubai. You can swing by the desert fort in Hatta, then hit Dubai for some camel racing and the maybe the gold souk. The drive to Abu Dhabi isn't very interesting, but hopefully you can find something to do when you get there. I've only be there for business meetings and don't know of any interesting things to do outside of the hotels.