A day trip to Nizwa- A few hours inland from Muscat is the historic town of Nizwa. Explore the souk which is best known for it's intricate silver jewelry and handicrafts. It has a huge castle as well which will surely enthrall you. I did not have time to do any road trips so I have another reason to go back to Oman.
The Wave - Spread alongside the wide coastline, it's a perfect place to leisure around, dine, enjoy the unobstructed ocean view and go on a shopping spree.
Muscat Gate - These are the grand gates that guard the national museum of Oman which displays it's history from Neolithic times to till date. It's very informative and will satisfy all your curiosities.