The Old Town: A couple of hours on foot in the old part of the city allows you to experience its unique spirit, the busy harbor, colorful houses, whimsical murals and sculptures, and interesting architecture, old and new. Start at the main tourist office on Reykjavik's oldest street at Adalstraeti 2, where you can pick up free printed walking guides. The points of interest are easy to find, roughly between the Old Harbour and the town pond (Tjornin on the map).

Along Tryggvagata, the street beside the harbor, at Posthusstraeti, an enormous mosaic depicts the city's maritime life. Keep strolling to see plaques with photos of old sailing ships, one of the old steam locomotives used to build a harbor railroad and the ultramodern concert hall rising above the harbor. Head south toward the pond on almost any street, and you'll be in the oldest part of town, passing brightly colored buildings with tin roofs. You never know where you'll encounter an intriguing small gallery, a humorous sculpture or mural. Around the pond are the modernistic City Hall on stilts and the 1881 classic stone Parliament.

If your schedule allows, you can take advantage of the guided, 90-minute walking tours sponsored by Goecco Outdoor Adventures, with guaranteed departures from May 15 to September 15 at 1 p.m. daily, departing from the Elding Whale Watching stand, located on the Old Harbour. Another free walking tour option departs twice a day from Laekjartorg Square at noon and 2 p.m. Led by university students, the one-hour tour visits the Althing Parliament, Hallgrimskirkja Church, Harpa concert hall and more. In both cases, all it will cost you is a tip for the guide.

Hallgrimskirkja Church: Not everyone admires the odd stair-step architecture, but there's no missing this unusual church, named after Icelandic poet Hallgrimur Petursson. Iceland's largest church, seating more than 1,000, sits at the top of a hill at the end of the shopping street Skolavordustigur. Take the elevator to the tower, which literally towers over the town, for great city views. The concrete form was designed by former state architect Gudjon Samuelsson and was supposedly inspired by volcanic basalt rock formations. On the grounds is a statue of Norwegian-born Leif Ericson, the Viking said to have discovered America 500 years before Columbus. It was a gift from the United States in 1930 on the 1,000th anniversary of the world's oldest Parliament, Iceland's Althing. On some days during the summer months, you may be able to catch a concert at Hallgrimskirkja (usually at noon). (Hallgrimstorg 1; 9 a.m. to 5 p.m. October through May and 9 a.m. to 9 p.m. June to September. Sunday service takes place at 11 a.m.)

Reykjavik Art Museum: If art is your pleasure, head to the Reykjavik Art Museum, but there's a catch: The museum is divided into three different locations. The most convenient is Hafnarhus (Tryggvagata 17; +354-411-6400; 10 a.m. to 5 p.m.), the contemporary art museum, housed in a former warehouse across the street from the Old Harbour. A special gallery there is devoted to the large, comic book-style paintings donated by the Iceland-born artist Erro. (Hafnarhus is open 10 a.m. to 5 p.m. daily, with extended hours until 8 p.m. on Thursdays.) The other two sites are short cab rides from the cruise dock or town center. Kjarvalsstadir (in Miklatun Park) is the oldest and largest, housing paintings and sculpture by well-established artists. (Flokagata 24; +354-411-6420; 10 a.m. to 5 p.m. daily.) The Asmundur Sveinsson Sculpture Museum and Park resides in a striking, contemporary, domed building and is named for the sculptor who designed the edifice and whose work is featured inside. (Sigtun; +354-411-6430; May 1 to September 30, 10 a.m. to 5 p.m. daily. There's a fee, but you can walk around the sculpture garden for free.)

Harpa Concert Hall: Located on the waterfront, this striking building, made of colored glass, opened in 2011 and is home to the Iceland Symphony Orchestra and Icelandic Opera. It is designed to look like a glacier and at night it is lit up like the Northern Lights. It hosts a variety of concerts, international conferences, trade shows and more. Two restaurants are onsite, as are two shops, one of which features a selection of Icelandic music. There are guided 45-minute tours four times a day for a fee. (Austurbakki 2; +354-528-5000; open daily from 8 a.m. to midnight.)

Reykjavik 871+/-2 Settlement Museum: This underground museum was inspired by the discovery in 2001 of the remains of a Viking-age longhouse. The museum uses stunning interactive displays, models and artifacts to bring the story of the city's earliest settlers to life. Tours can be scheduled with English-language guides. (Adalstraeti 16; +354-411-6370; open daily at 9 a.m. or 10 a.m., depending on the season, and closes at 5 p.m.)

Shopping: Laugavegur and intersecting Skolavordustigur, the main shopping streets, are well worth strolling even if you don't plan on buying anything. The shops display not only the traditional Nordic sweaters but also the modern design that is an increasing influence in Reykjavik. As you browse, don't forget to look toward the water at cross streets for striking views and murals in unexpected places.

Iceland's Golden Circle: These tours offer a chance to explore the island's raw and rugged interior. The trio of sites includes the Strokkur geyser, where jets spout anywhere from 60 to 100 feet; the mystically beautiful Gullfoss (or Golden) falls, Europe's largest waterfall, tumbling into a glacial river with a 105-foot double cascade; and Thingvellir, a scenic national park that marks where Europe's first Parliament, the Althing, was formed in 930 AD. Your best bet is to book a tour, whether through your cruise line or via an independent company like Tours By Locals. One of the best ways to tour the interior is in an off-road vehicle that crosses unbridged rivers to get to the more remote locations.

The Blue Lagoon: Located about 40 minutes from downtown, the Blue Lagoon is one of Iceland's most popular destinations. Steaming, mineral-rich hot water from far beneath the earth forms this spectacular man-made lagoon, amid a rugged lava landscape. A health spa also offers mudpacks and massages. The lagoon's geothermal water is believed to be beneficial for everything from skin problems to arthritis. Keep in mind that, while the Blue Lagoon is well worth a visit, you probably won't have time to enjoy the hot waters and explore the city of Reykjavik. (Grindavik 240; +354-420-8800; open daily from 9 a.m. to 9 p.m. June, July and August and from 10 a.m. to 8 p.m. September through May.)

Thermal Pools: Reykjavik is famous for its steamy geothermal swimming pools, fed by underground springs. The biggest and best-known is the Laugardalslaug with both indoor and outdoor pools, plus "hot pots" and a thermal steam bath for those who really like it hot. Take a cab or the #14 bus. The pool is part of Laugardalur, the city's largest park, where you can easily spend a rewarding day. The park includes botanic gardens -- showing off local plant life and great displays of seasonal flowers -- as well as the city zoo. Editor's Note: In order to keep the pools clean, all visitors to any of Reykjavik's thermal pools must wash thoroughly with soap (and without a swimsuit) before getting in. (Sundlaugavegur 30a; +354-411-5100; Monday through Friday, 6:30 a.m. to 10 p.m.; Saturday and Sunday, 8 a.m. to 10 p.m.)

Arbaer Open-Air Museum: Operated by Reykjavik City Museum, Arbaer Open-Air Folk Museum is a period farm turned into an open-air museum with more than 20 buildings forming a town square, a village and a farm. Most of the buildings have been relocated from central Reykjavik. Craftspeople demonstrate traditional farm-life crafts and chores. Although it's located in a suburb of Reykjavik, the museum is easily accessible. Take bus #19 from Hlemmer, the main bus station on Laugavegur, and ask to get off at Strengur, a quick walk from the museum. (Kistuhylur, 110 Reykjavik; +354-411 6300; Open daily from 10 a.m. to 5 p.m. June, July and August. September through May, the museum opens at 1 p.m. for guided tours only.)

Puffin Tours: Boat tours take visitors past Puffin Island, where thousands of these adorable birds are found in mating season. Puffin Express has tours to the islands of Akurey and Lundey, from May 1 to August 20, using small boats that bring you close to shore. Check kisoks at the Old Harbour for details.