Sur is 350 km south-east of Muscat, a drive of roughly four hours along Route 23 (the Quriyat–Sur Road), which hugs the coast for much of its length through dramatic scenery — cliff roads, fishing villages, and the sharp escarpment of the Hajar mountains dropping to the sea. The drive is genuinely good; don't rush it.
There are regular buses between Muscat's Ruwi bus station and Sur. The journey takes around four hours. A rental car gives you much more flexibility for reaching the wadis and the turtle beaches, which have no public transport.