Personally, I would avoid Avon schools. My girlfriend is a foster mom and she had alot of problems with the elementary and the high school. I hear Plainfield schools are good. Is there a reason why you have to be on the west side of Indy? My daughter lived in Plainfield and loved it. She moved to Spencer with her boyfriend, however, he was killed in a head on collision. My daughter plans to move back to Plainfield once she has healed from the accident.
I live in Fishers which is NE of Indy, which is Hamilton county and Hamilton Southeastern Schools. My son has had no problem with the schools.
There are nice areas on the west side of Indy. I grew up on the west side and went to the Wayne Township Schools, including Ben Davis High School. But, that was 25 years ago and it has changed so much. I cannot recommend or not recommend that school system. My daughter did graduate from there in 2003. She liked it there ok. Her daughter goes to Garden City which is in this school district. It is very multi cultured which she likes because it is exposing her daughter to many different types of people. Some people don't like that, it's a personal preference, in my opinion.
Good luck to you, I know it's hard to know what is best for your child/children.
Keep us posted on where you decide.
J.