If you've got money to spend, look into Beijing-based Imperial Tours, with packages starting at $1,000 per person, per day. As part of its three-day tour of the Jinshanling section of the Wall, which sees only about 10,000 visitors a year, guests walk into a turret scattered with rose petals and enjoy a gourmet meal on top of the Great Wall.
If you're short on time, it's fine to visit the tourist-friendly Badaling, but you must do it first thing in the morning. It opens at 6:30 a.m. in summer and 7 a.m. in winter. There's a public bus that can take you there, but to maximize your time and experience, consider hiring a driver to get you to the Wall the minute it opens. This advice holds true for many of the world's great sites: the Pyramids in Egypt, the Taj Mahal in India and Machu Picchu in Peru are all—by far—best experienced before the crowds descend.
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In other major attractions, the key is to find alternate ways to get a similar experience. You'll have trouble getting a dinner reservation at Le Jules Verne restaurant atop the Eiffel Tower, but the iconic restaurant is also open for lunch when it's much easier to get a reservation. Book lunch on a weekday and you'll save yourself a lot of hassle—not to mention expense—while experiencing sweeping city views in the daylight.
Peter Greenberg's best tried-and-true tip for avoiding crowds