Choose a space that works well for your situation, with the most important factors in most cases being: Ease of access, early morning sun, and for the urban and suburban beekeeper, concealment/protection from neighbors. You'll want plenty of room to get behind the hive to inspect the colony, or peer in the window if you are using a horizontal top bar hive.
The idealistic beekeeper's checklist includes the following "requirements": Southeastern exposure, early morning sun, afternoon shade, wind barrier, dry, flat ground, close to a water source, easy access and concealment from neighbors. However, many beekeepers don't have a place that meets all of these requirements - never fear, honey bees are incredibly adaptable creatures. We've encountered numerous feral colonies in locations that don't meet ANY of these requirements and they were thriving.
If you are in a neighborhood that may not share your passion for beekeeping, we recommend placing the hive in a fenced area. To prevent the bees from using your neighbor's yard as a freeway, you may want to face the entrance of the hive toward a tall object such as a fence, hedge or the wall of your house. This will force the bees to adjust their trajectory and fly upward and high above your neighbor's houses.
Lastly, you will want a space that is close to a water source (preferably not your neighbor's pool). Bees are highly efficient insects - they aren't going to fly 50 yards to your bird bath if your neighbor's pool is 5 yards away - much to the frustration of your neighbor. Be sure to place a water source with gently sloping sides within 50-100 feet of your hives so that they can access the water for cooling and/or mixing with pollen to create bee bread.
While there are many "requirements" on the traditional "hive placement checklist," I think one of the most important factors to consider is ease of access for you, the beekeeper. The bees are adaptable, and can overcome just about any inconvenience you throw their way. If the location makes it difficult for you to enjoy the hive, and especially if it makes it difficult for you to work in the hive, this is a major issue. You will want a location that is free of obstructions on the backside of the hive (the side with the window), with at least 2-3 feet of space so that you can stand and squat comfortably. I assure you that you will spend more time than you know knelt down with friends and family while eagerly looking through the window to see the progress your bees are making. Try and provide enough space for at least 2-3 people to fit comfortably while looking through the window.
Horizontal top bar hives are foundationless, and the bees build their comb perpendicular to the ground. If your hive is on a slope, the comb will be equally sloped. Make sure you either place the hive on level ground, or place garden tiles, rocks or scrap wood under the legs to make it as level as possible. This also makes it easier for you to access the hive without fumbling up and down a hill.
While this doesn't apply to extremely hot areas, it is generally agreed upon that hives are more successful with more sun than less. If you have to choose between early morning sun and afternoon sun, go with early morning sun, as this will get the hive active earlier in the day, and provide them with more time to gather resources.
If you live in an urban or suburban area and you feel there is potential danger to either the bees or people, be sure to place the hive in a relatively concealed area -- preferably one that is fenced off. Many beekeepers who live in the city like to point the entrance of the hive toward a fence or a hedge
Wind: Ideally the hive will be placed in a location that is protected from harsh winds billowing into the hive entrances during the winter. Due to the leg configuration and weight, our hives are very sturdy and we've had no issues with hives being toppled by high winds.
If you live in an arid region -- especially one where pools are prevalent -- this is consideration is more important. Bees need water to use within the hive, and they, being opportunists, will frequent the closest reliable water source, regardless of how inconvenient it is for you or your neighbors. If the closest water source is your neighbor's pool or bird bath, the bees will be more than willing to use them. If this matters to you, make sure you provide them with a shallow-sloped water source. Bird baths work very well!
Obviously if you plan to keep bees in your back yard you will have little control over the nectar and pollen sources available to your colony, but an important consideration nonetheless. We've had greater success with our colonies placed in urban and suburban areas, largely due to the abundance and variety of flower plants available in parks, gardens and yards. Rural areas, especially areas with heavy agriculture, generally have less forage available due to the use of mono crops, pesticides and fungicides.
The last, and maybe one of the most important factors, is whether it is legal to keep bees in your area. Many cities still outlaw beekeeping outright, or make the licensing process incredibly difficult for the beekeeper. Check your city, county and state laws prior to investing in a beehive and bees, and then make a decision accordingly. Keep in mind that a number of areas have antiquated laws explicitly banning the use of any hives but Langstroth or frame beehives.
While I don't know of anyone being accosted over such silly regulations, it's still something to keep in mind.