Copenhagen's luxury hotels, clustered in the stately Amalienborg district and near the Strøget, favor a modernist style that reaches its apex in large hotel complexes such as the First Hotel Skt. Petri. That means grande dame hotels aren't as prevalent here as in other European cities, although the landmark D'Angleterre and plush new Nimb fill the void. If you're looking for a hotel room under $300 per night, try the homier harbor-front hotels surrounding the Nyhavn (such as 71 Nyhavn), or one of the whimsical Vesterbro properties that feel more like bohemian guesthouses than hotels (Bertrams Hotel Guldsmeden, for instance). If a bargain is more important than atmosphere, look to the cheap, generic hotels near the central train station and Tivoli—the Danhostel falls on the stark side of minimalist, but it's among the best buys in Copenhagen, and you get a private bathroom with your dorm-worthy bed.
Copenhagen has plenty of beds for a city its size, but the best hotels tend to sell out in summer high season, and occasionally when Scandinavian conferences come to town. Check with VisitCopenhagen.com for information on upcoming events before planning your trip—the tourist board's Web site also has an up-to-date booking service and lists affordable short-stay apartment and single-room rentals throughout the city.