I grew up in Memphis, and I would say move to East Memphis. Between Park Avenue and Walnut Grove are the best areas, but may be a little pricey. A lot of my friends, that range from young professionals, newly weds, and younger parents (35 and under) have bought houses in the High Point Terrace neighborhood. This is a really cute area, and is about 15 minutes to downtown, and about 15 minutes to Germantown. I live in Chattanooga, and have thought about moving back to Memphis recently. If I had children, I would 100% live in East Memphis. It is part of the city, however, in my opinion, it is the best part of town to live in. Maybe I am just biased because this is where I grew up, but if you like houses with character that are not all "cookie cutters," this is the area to live in.There are lots of parks, shopping, restaurants, a really nice movie theatre and other amenities that you may really like. The public school system is not the greatest in Memphis, so you need to be aware of this when looking for a place to live. White Station is a good public school, and Grahamwood is a great public elementary school. I went to a private school, (St.Mary's) however, I would send kids to either one of these schools. The best way to describe East memphis is the suburb in the city.
Germantown is great too, but the houses are much newer and do not have as much character. It is common to see houses that are all practically identical to one another all along a street. The public schools are good in Germantown, and this is a really nice area as well. Poplar Avenue and Poplar Pike pretty much run right into East Memphis. Cordova is not a bad area either, but it is not quite as nice as Germantown. You will definitely hit a lot of traffic on Germantown Parkway, at almost all times of the day. This is one thing to think about... it is the main road that connects Cordova (and Germantown) to the rest of the city. I hope this helps!