As Salaam Alaikum
Don't live in the boundaries of the Indianapolis Public School system. Even if you send the kids to private school, the area is most likely not going to be safe to live in. There are very dangerous areas around IUPUI and all throughout Indianapolis. Do not live near the Lafayette Square Mall area.
If someone has committed some types of sexual crimes in the United States, that person has to register their address. It is public knowledge. You can go to a website and put in the address where you want to live, and then the website will show you where sex offenders live and work near that address. Every address will have some sex offenders nearby, but some will have many. You don't want to live near many. In the good neighborhoods there will be none or very few nearby.
People have to register for many different types of sexual offenses, and in the US some are considered much worse than others. You can see a picture of the person and read what their crime was. That way you can make sure your family does not play near that person. Here is the website:
Indiana Sheriff's Sex and Violent Offender Registry
You can also be very friendly with the local police department and they will be happy to tell you which areas are safest to travel to. You should definately ask the local Arab groups about what kind of behavior is socially nonthreatening here. If you were in the wrong area you would need to be careful not to look at other people in the wrong way.
Others have suggested Plainfield, and that is not a really long commute from IUPUI. Maybe about a half hour? Avon is there, too. I think you may feel more comfortable living in a suburb and driving in, especially with your wife having a young child. She will want to take the children out to play with other children and other mothers, and that is just easier in a suburb.