Um, no. Not in the case of Levittown.
Just after WWII, suburbanization was driven by the fact that a) there had been a terrible, deep and long recession just prior to the war 2) during the war, with two income families unable to have kids because hubby was off at war overseas and wifey was working in a factory at home, savings rates approaches 50% for some parts of the war (in part due to rationing -- people were encouraged to grow vegetable gardens so that what farmers grew could go to feed our soldiers overseas) 3) women who had been recruited to work in factories during the war were encouraged to go home and have babies and be full time wives so the returning soldiers could get jobs (and many women were very happy to do that) 4) a very high percentage of men had served in the military and now qualified for federal help with getting a house, as well as federal help with going to college.
This is the roots of the sudden large middle class you saw in the 1950's. And that is the root of the high demand for housing, which America worked hard to meet in record time. We are still living with the legacy of that decades later when our demographic has changed and it no longer serves us that well.
I have no doubt that this benefited whites more than blacks. But it was not rooted in whites trying to get away from blacks/cities/whatever per se.
Edit: My point about Victory Gardens was about the impact on personal finances. They also rationed sugar, cigarettes and other things. The point is that there were a lot of two income families who were not having children and there were also no luxury items to buy during the war. So personal savings rates were crazy high.