Copenhagen has an air of cool about it. Amid the quaint cobblestone streets and picturesque canals, Denmark’s capital — and Scandinavia’s largest city — has the unmistakable buzz of a place that’s always churning out something exciting and innovative, whether it’s a hip, new restaurant or a groundbreaking décor design.

Start your day at Radhuspladsen, the Town Hall Square, and stroll down Stroget, Copenhagen’s famed pedestrian shopping street. Amid familiar shops like H&M and Aldo, you’ll find unique retailers like the well-known Danish design mecca, Illums Bolighus (Amagertorv 10, tel 45 33 141 941).

After that, head to the water. The best way to see Copenhagen is, undoubtedly, by boat, so a canal tour is a must. DFDS Canal Tours (tel 45 32 963 000, http://www.canaltours.com) leave approximately every half hour and offer multi-lingual commentary throughout the hour-long ride. As you float along, you’ll see tourist sites, such as Amalienborg Palace, where the royal family lives, and the famed sculpture of Hans Christian Andersen’s Little Mermaid. You’ll also pass new attractions like the massive, modern, new Opera House. But just as enjoyable are the glimpses you’ll catch into everyday Copenhagen life: In narrow inlets, some barely wide enough for the canal boat, you’ll pass by locals relaxing and picnicking on boats docked right outside their residences.

Once you’ve come ashore, head to Nyhavn for lunch. This narrow waterfront inlet, formerly dubbed “the longest bar in Copenhagen,” was once a hangout for sailors and vagabonds. Now it’s cleaned up and known for its alfresco restaurants. Stop into Nyhavns Faergekro (Nyhavn 5, tel 45 33 151 588) for Danish smorrebrod. These tasty, open-faced sandwiches come in scores of varieties, such as double-smoked salmon and small bay shrimp, served atop slices of homemade bread.

After you’ve refueled, spend some time catching up on your Danish history — from the Ice Age to the Vikings to present-day — at the Nationalmuseet (Ny Vestergade 10, tel 45 33 134 411), where admission is free. If time allows, make your way up the spiral walkway of the Rundetaarn, or Round Tower, a 17th century astronomical observatory (Kobmagergade 52, tel 45 33 730 373). From the top you’ll enjoy panoramic views of Copenhagen.

For a casual evening meal, try BrewPub Kobenhavn (Vestergade 9, tel 45 33 320 060). This microbrewery, just off Radhuspladsen, changes its menu with the seasons — main courses for the spring included grilled veal steak with polenta and pork cheeks with smoked potato terrine — and infuses many dishes, such as the hop sorbet and chocolate soup, with its ales, some of which boast colorful, musical names such as James Brown Ale and Cole Porter.

After sunset, gather with the locals at Tivoli Gardens (Vesterbrogade 3, tel 45 33 151 001). From outside this historic amusement park’s walls, Tivoli doesn’t look like much. But once you’re inside the gates, it’s hard not to feel like you’ve been transported into a childhood fantasyland. Walk the grounds and take in the live music and tiny lights illuminating the picturesque park. If you’re feeling daring, top off your night with a ride on the Daemonen roller coaster or the giant, spinning Star Flyer swings.