The Muttrah Corniche that sweeps around the edge of the harbor is the center of all activity, especially on a Friday night after evening prayers, when locals take to the streets to promenade, meet friends, eat and drink coffee. By day, there are frequent shady places to rest, and the whole promenade is lined with cafes and restaurants, some with outdoor seating.

About half a mile from the port shuttle drop-off point is the Muttrah Souk, the old Arab market, which is part-tourist attraction and part old-fashioned shopping mall. You can smell the incense even before you plunge into the narrow alleys, a treasure trove of spices, artifacts, silver daggers, pashmina shawls and all manner of incense burners. Most of the tours don't allow much time in the souk, but it's easy enough to go back on your own, as it's open until late in the evening. Compared to other markets you may have visited, the hassle is minimal; although traders by nature, Omanis are gentle and dignified people and will not harass tourists.

The Sultan Qaboos Grand Mosque in the modern part of town is breathtaking and is a feature of every city tour. If you go independently, it's open to non-Muslims from 8:30 a.m. to 11 a.m. every day, except Friday. The dimensions and the detail are awe-inspiring: 20,000 worshipers; acre upon acre of cool, white and grey marble reflecting the harsh sun; an exquisite Persian carpet in the main hall that took 27 months to hand-weave; chandeliers bearing thousands of crystals; and tranquil gardens with tropical flowers and splashing fountains. It's essential to dress modestly to enter the mosque -- women must cover absolutely everything.

A trip to the mountains presents a different face of Oman, bumping in a 4x4 along dusty riverbeds between towering cliffs of red sandstone, stopping to swim in deep, crystal-clear wadi pools and picnicking under shady trees at lunchtime. Either book through your cruise line (they all offer this tour), or consult the Cruise Critic message boards for recommendations of independent operators. There are countless tour operators in Muscat offering this tour to travelers, and they all follow much the same itinerary.

Head inland and tour some of the ancient forts built by the Portuguese. Nizwa is the old capital of the interior and offers the unlikely combination of a solid, 17th-century fortress with an enormous tower and sweeping views of the desert and mountains. There's also a new, air-conditioned souk. This is the place to buy dates, herbs and spices, silver daggers and Bedouin jewelry. It's also the place to inspect, rather than take home, fresh fish.

Oman is known for its whale- and dolphin-watching; the sea is deep and clean, with an abundance of food sources, so the chances of a sighting are good within relatively close distance of Muscat. Most cruise lines offer day-trips. Muscat-based tour operators also offer this trip to independent travelers, but always check that your operator conforms to the guidelines suggested by the Whale and Dolphin Conservation Society, which help protect the wildlife.

Separate trips offer snorkeling on the coral reefs, combined with a spell at a beach resort. All the beach resorts are located out of town (there are no swimming beaches in Muscat itself), and a typical tour involves a boat trip with snorkeling, followed by beach time at one of the resort hotels. You can purchase refreshments from the hotels, as well. Although Oman is a conservative country, normal swimwear is acceptable on the beaches within the confines of the resorts, although sunbathing topless is a definite no.

With an overnight in port, take a private tour to the Wahiba Sands, the desert landscape of movies: rolling dunes, green oases and camels galore, overnighting in a Bedouin camp or in a hotel.

It's also possible, on a separate trip, to overnight at Sur, famous for its turtle nesting grounds, and embark on a turtle-watching vigil at night as the females come ashore to lay their eggs. Contact an Oman specialist like Panorama Tours for this.