Whether you have your children full time, half the time, or every other weekend, you are considered a single parent. This is an important distinction to make as you move to a new city as single parents must have much higher criteria for their new apartments than adults who do not have children to worry about. There are many things that a struggling adult will deal with while trying to set up a new apartment and a new life in a new city, but when there are kids involved it is the needs of the children that dictate what you do and where you live.
You can get a good feel for any neighborhood while looking for apartments for rent in Atlanta just by driving through a few times. If you drive through once at night, you can check for activity that would make you nervous if you lived there such as gang or criminal activity. If you take a drive through during the day, you can check out atmosphere of the after school hours as well. See where the kids there are playing and if anyone seems to be paying attention to them. What else is near by? Are there any museums or libraries? Is there a grocery store close enough to walk to?
Lastly, it is important to know what kind of school choices your child has for that location. An independent nearby private school can be great if a parent can afford it. A place like the YMCA that offers classes and lessons for kids on afternoons and weekends can be helpful as well. It is not easy for adults or children to adjust to living in a new city. But if you take the time to make sure your new neighborhood is a good fit for you, the transition will go much more smoothly.