Safe day and night, even for female solo travelers. 99.9% of locals are nice and welcoming and willing to help to best of their abilities but I would be weary of taking random lifts while hitchhiking.

Oman is an incredibly safe country, with a very low crime rate and virtually no violent or petty crime. The people are warm, friendly, and welcoming, especially towards foreigners, and all religions are respected. While walking around, you can feel safe even at night, though. There has been instances where i have been catcalled or followed but without any harm or interaction. However, these occurrences are rare and do not diminish the overall sense of security in the country. It is one of the most peaceful countries in the world.

Muscat is a safe city. I would often take a stroll at night with no worries, as the hospitality-centric culture of the people reassures my worries on my safety. The only uncomfortable thing I would get is stares by other foreign workers.