The city is actually three smaller cities combined which makes things confusing and also time consuming if you’re not in the right part. Muscat is known as the walled city whilst Matrah is the other part of the city of interest to tourists.
Al Jalali and Al Mirani forts were originally prisons built outside the city by the Portuguese in the 16th century. As the city expanded they came within the city limits and today have been converted to museums. The Qasr Al Alam Palace is stunning and the home of the Sultan Qaboos, the Omani ruler. It’s not possible to see inside the palace but you can take photographs of the heavily guarded exterior and its position at the head of an attractive natural harbour.
For an interesting experience you can have tours of several factories in the city. The best of them are the halva factory where they make the delicious sesame sweet and the perfume factory where the world’s most expensive perfume, Amouage, is made.