Icelandair offers flights to Hamburg multiple times a week.
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The Rathaus and the red-light Reeperbahn, fish market and flea market, harbor tours and HafenCity - Hamburg will keep you busy. The elaborate Rathaus (town hall) is a good starting place: it was built in the 1890s, when Hamburg was flourishing as a trade port. Contrast this with the dazzling, ultra-modern Elbphilharmonie concert hall, a landmark seemingly topped by a giant glass wave. Visit for a stellar city view.
More architectural highlights are in the warehouse district of Speicherstadt. These enormous red-brick complexes have Unesco World Heritage recognition, and a boat tour offers a scenic way to appreciate them. Bucking the trend that bigger is better: Miniatur Wunderland is an incredibly popular model railway exhibition, and a truly magical attraction that's rich in detail.
There's no escaping the seafaring heritage of the city at Hamburg's noisy, atmospheric Fischmarkt in St Pauli, a city institution since 1703. It requires an early start (it begins at 5am). Get a fried-fish sandwich for a real taste of the city - there are vendors all over, especially around the port. Another uber-local taste: Franzbrötchen, a flat criossant laced with cinnamon.
Close to Speicherstadt, the cobbled Deichstrasse is good hunting ground at dinnertime; for a fresher feel, hit the uber-cool Sternschanze neighborhood (also known as Schanzenviertel or simply Schanze). In summer sunshine it's hard to beat a picnic in the flower-filled Planten un Blomen park. For picnic fare and leisurely grazing, check out the twice-weekly Isemarkt in Eppendorf - it's one of Europe's largest farmers markets, with some 200 stalls stretching an impressive half a mile.
One of the best shopping stops is the Flohschanze, a Saturday flea market held along Neuer Kamp street in the Karolineviertel, just south of Sternschanze. Take a stroll around this area for fun shops and cafes with a creative, hipster vibe.
For a different feel (and catering to a different budget) is the boutique-laden, arcaded Jungfernstieg promenade, joined to the city's mainstream shopping strip, Mönkebergstrasse, by the large Europa Passage mall. Be sure to cruise Neuer Wall to see Hamburg's prosperity first-hand - this strip is almost wall-to-wall luxury brands. For something more local, the street named Lange Reihe near the central station has a couple of stores selling cute, Hamburg-made items.