The area of Lithonia you move to depends in what you can afford of course and you didn't specify that I will just give you some areas in different ranges.
There is a ton of new construction in Lithonia as I am sure you've seen. If you are looking in the mid 100s to the low 300s range then I would suggest checking out the areas to the north of Stonecrest Mall (Rock Chapel Road, South Deshon Road, Rockbridge Road, South Stone Mountain-Lithonia Road). Lithonia is one of those places where you can get the most for your money. For $250,000 you can get a five bedroom, four bath brick front home on a half an acre.
Upper income neighborhoods are scattered all over Lithonia and are not concentrated in one specific area. If you are looking in this range(400+) I would suggest moving south of I-20. Roads in these areas include Brown's Mill Road (where the infamous Sandstone is located), River Road and Flake's Mill Road. John Wieland is also building a new subdivision off Dogwood Road which starts in the 400s.
No matter your price range there are good solid homes you can buy in Lithonia. As for crime, that's all relative. People in Buckhead have their homes broken into too. Lithonia's crime is not as bad as inner-city Atlanta and I promise that if you were to visit these subdivions you would feel like you are in a peaceful suburban enclave instead of feeling like you have to be loking over your shoulder every five minutes. I live in Vinings and have been robbed before so stats don't really phase me that much anymore. If there were only three robberies in my area (I have no idea what the real number is), out of the 12,000 who live in my community, the stats would seem low and everyone would tout Vinings as such a safe place to live. But I would be complaining about the
crime problem because my home was broken into! There is crime everywhere, Lithonia on the whole is a safe place to live and if a crime is committed against you it is just due to chance as i cited in my example.
As for schools, they are substandard in South Dekalb right now compared with those in other parts of the metro area. If private school won't be an option, I still wouldn't shy away from the area considering how much you can buy for the money. There are improvements being made. There is an IB progam now at MLK High available to all kids in South Dekalb. Also you should look at sending you child to Kittredge. It's a magnet elementary school available to all who live in Dekalb County. It is very competitive however and it's admissions process is more in line with a private school. BUT it is one of the top, if not THE top elementary school in the state. Students from Kittredge continue in the magnet program to Chamblee Middle and Chamblee High. Chamblee High School is the best in Dekalb and one of the best high schools in the state as well. I'm saying all this to say that one would have options if the schools in their area are sub-standard and can't move to the better school districts because of pure choice or affordabilty. There might be even more options or magnet programs but since I do not live in Dekalb County I am not sure of any others.
Also, you might find it interesting that Lithonia is 79.61% Black. The median income for a household in the city was $97,506, and the median income for a family was $135,450. Males had a median income of $87,585 versus $85,100 for females. The per capita income for the city was $77,650. While it has it's blighted area's, as you can see, the city on the whole is a prosperous place to live. I got this information from wikipedia:
Lithonia, Georgia - Wikipedia, the free encyclopedia
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Ready to Move...
I live in Lithonia which up until about 2 months ago I thought was just a great place for me to be...witin the past 2 months a neighbor of mine has been robbed,cars broken into in the parking lot of the apartments that live in and just more activity going on that was not here before. 
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