The Indian Ocean is a divers paradise with clear blue waters that are a joy to swim in. There are some good reefs just off the coast, and most hotels will be able to arrange a diving trip through a licensed school.
The Hajar Mountains run down the middle of the country, and while the loose rock that makes them up is unsuitable for climbing, there are some walking trails to follow, and dried up river beds, or wadis that are thrilling when driven along by an expert in a jeep or other 4WD car, it's called Wadi Bashing, and is something of a local tradition.