Look for any apartment finder services in your area. If you are in a city of appreciable size, then you most likely have at least one.
From my experience with them, these guys are often free and pretty efficient at locating within your parameters. I've always had them come back with exactly within my budget in just the right sort of area I asked for. Of course, you'll still need to use your own discretion to weed the choices they provide (they exist to narrow down your choices, not make them for you, and if they try to go salesman and make them for you, it's your job not to fall for it), but they are helpful.
Some caution though. First off, as I said, I've always found these services to be offered for free. Of course, some will demand fees. Look for the free ones if you can, but understand that the free ones are going to be sponsored by the real estate of the local area most likely. After all, they aren't doing this out of the kindness of their heart. The apartments are paying them to bring people to the lease. In other words, again, you'll need to use your discretion to determine if the apartment fits you.