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Geography is an important consideration when choosing a hotel in Stockholm. Unless you have a good reason for hiding out in the suburbs, I'd recommend picking a hotel in:
Blasieholmen and Ostermalm
Hotels like the Diplomat (see above), the Grand, and the Radisson SAS Strand are convenient to sightseeing, shopping, and transportation. They also let you enjoy the boat traffic and vistas along the city's clean, attractive, and lively waterfront.
Stockholm's old town is an attractive melange of narrow streets, busy restaurants, and small shops. The Royal Palace is located here, and you can easily reach downtown Stockholm on foot or by a Tunnelbana subway line. The Reisen is a great choice in the upscale category; for something different, try Malardrottningen, a floating hotel in what once was Barbara Hutton's yacht.
Much of the area around Stockholm's central railway station was torn down and replaced by modern buildings in the 1960s, so atmosphere isn't this district's strong point. Still, if you're in Stockholm for only a day or two, a centrally located hotel such as the the Nordic Light or the Nordic Sea (home of the famous Ice Bar) is undeniably convenient. If you've got money to spend, reserve a room or suite at Berns' Hotel, a stylish boutique hotel that's just outside the business district near department stores and the Berzelii Park.
This large island just to the south of Gamla Stan is reasonably convenient if you're staying at a place like the Hilton Stockholm Slussen, the Clarion, or one of the floating youth hostels near the Slussen Tunnelbana station. You'll probably end up taking public transportation to many of the sights. But in the evening, you'll find an endless choice of bars and restaurants in Stockholm's trendiest neighborhoods (including "SoFo," which is south of Folkungagatan and east of Gotgatan).
Other islands in Stockholm
Hasselbacken, on the museum and park island of Djurgarden, might be appealing if you're honeymooning or traveling with children in the summer. The af Chapman youth hostel (a converted three-masted sailing ship) is worth the walk to Skeppsholmen if you'd like to be near the town center but can't afford a room in Blasieholmen, Ostermalm, or Gamla Stan. To serve time without a crime, book a cell at Langholmen on the park island of the same name; the converted 19th Century lockup has a hotel and a youth hostel on the premises.
For more information on where to stay, visit the Accommodation in Stockholm pages at the Stockholm Visitors Bureau's Web site. And for low-cost lodgings with a personal touch, search for a private room at Bed & Breakfast Service Stockholm.