Of course, there are a number of classic sights in Oman, some real highlights, whose visit should be planned depending on the time and itinerary. You will find the most important of these listed under the above links.
However, Oman's culture lacks anything pretentious, loud, there is not the tallest skyscraper or the most expensive necklace to marvel at. Oman means: seeing colours, breathing fragrances, sensing horizons, physically experiencing extreme contrasts, seemingly losing oneself in endless, even archaic landscapes, and in any case: experiencing friendly people.
So if you move around the country with your senses alert, if you don't tie your travel schedule too tightly, if you take time for a conversation that arises from time to time, and if you thus encounter the seemingly trivial things in life with leisure, you will leave the country full of unforgettable impressions.