You don't even need to ban cars, just add traffic calming that makes the route less convenient for people driving through it. My town did this with a section of a street that went through medium density housing. They changed it from a three-lane one-way street to a two-lane, two-way road with two bike lanes and replaced the stop lights with roundabouts.

Now driving through there takes twice as long as before, which motivates drivers to avoid the area. Since it's now just the people who live in the area there's a lot less car traffic. And it's reasonably close to downtown with plenty of stuff within walking distance.