Gazebo location is going to depend to a large extent on what you are planning to use your gazebo for. Is it a garden gazebo, a gathering place for friends and family on beautiful summer afternoons? Perhaps you'll be enclosing your gazebo and installing a hot tub or spa inside of it. How you use your gazebo will determine where you should build it. A garden gazebo might be located toward the back of your yard, in order to have friends walk through it. A hot tub shelter should probably be located closer to the door, to minimize the walk in a bathing suit.
Aesthetics are important: you may choose to highlight your structure by making it the center of attention or blend it in to your landscape and make it a secret hideaway. You should also be mindful of the building's relation to other structures that you may have on your property.
Think about the pros and cons of your preferred site in all four seasons. The surrounding foliage (and weather) can look very different from one season to the next. All of these considerations may have some impact on where you build your gazebo.
Choosing a size for your gazebo is the next important step. The key is to ensure that your space is large enough for its intended purposes, while remaining proportional to the surrounding environment. A general rule of thumb is that an 8' gazebo fits 2 people (2 chairs) and a small table. With every two-foot addition, two more people can be seated comfortably in the gazebo (for example, a 10' gazebo holds 4 people comfortably, a 12' gazebo holds 6 people comfortably, etc.).
Once you have decided on a size, it's a good idea to stake it out the dimensions in your yard to ensure that the fit is comfortable for your needs and that the location is harmonious with your landscape.