Once you have selected a quarter of the city, you can refine your search by choosing a neighborhood within that quarter. By "neighborhood," I mean the three to five block area immediately surrounding the place you might live. These few blocks are going to play a big role in your outlook and experience. You will have a different view of the same quarter of the city if your neighborhood is near a placid park or at the crossroads of a noisy intersection.
Your final choice of your neighborhood will probably depend on the housing available. Therefore develop a list of up to three to five neighborhoods in your target quarter where you will look for a home.
TACTIC: List what you want to have in the nearby environment of your neighborhood.
Consider what you need: A view? Quiet? Activity? Shopping? A transit stop?
TACTIC: Look for neighborhoods that are walkable.
Find sidewalks, marked crosswalks, and pleasant pedestrian spaces. Is it possible to cross the streets? (In the suburbs, there may be streets specifically designed so that pedestrians cannot cross them). The most efficient form of transportation is walking--see how different neighorhoods support this.
You can examine an area where you want to live and quickly see if it would allow you a choice of many different types of transit. You can see from this photo that you would not be able to walk easily through this neighborhood. In fact, this street is designed for cars, and a person biking or walking might find it difficult to traverse. These types of neighborhoods lock you into one transit mode--an automobile--for just about every trip. This complicates your life by wasting time and resources and not giving you a chance to exercise.
You can look at the neighborhood and see what people do there--in this case, drive in cars.
You can see sidewalks, people walking, a sidewalk cafe, bicycle parking, and there is transit nearby. This type of neighborhood will allow you the freedom to choose transit modes for different kinds of trips--walking, bicycling, the bus--and go about your life. You could walk to cafes, perhaps your work or schoool, and gain access to the resources you want more easily and in a way that helps you exercise and enjoy the life of the city.
To find walkable places, of course, you can just walk around a city and see what makes you feel comfortable. To do some informal research, you might even ask suburbanites in the region, "Where is it hard to find a place to park?" Their answers will help guide you to walkable areas. Places that are hard to park are interesting places that place less emphasis on automobile storage (therefore making it harder or more expensive to park) and that are therefore likely great places for pedestrians. If you see massive amounts of free or cheap surface parking in a neighborhood--stay away--that indicates that city officials or even businesses in the area are more interested in storing cars than in supporting walkable urbanism. In brief, go for places that suburbanites hate and stay away from places that suburbanites love because of cheap, plentiful parking.
TACTIC: Look for neighborhoods that offer access to stores and services that meet many of your routine needs.
For example, find a place to buy groceries, a cup of coffee, get a haircut, have a meal.
In evaluating a place to live, see how many nearby places you can walk with walkscore.com. This site gives you a quick overview of how many places you can walk from a particular address. This site itself admits its limitations, and you'll need to further consider the places it comes up with based on your own valuation of them. However, this site is a very good way to quickly get a dramatic sense of how where you live impacts where you can walk.