On the west side, around 465, the gang activity was all the way up to 65th street 10 years ago. If you are going to live close to Indy on the west side, start from 65th and work north and west outside of 465.
From 10th to 38th should be considered off limits, including parts of Speedway. But then again I have friends who live in the middle of that area. I just don't see getting off to a good start living in that area of Indy. If I am on the west side, I am in Plainfield. Damn near bought out there back in 92.
There are some apartment complexes right along 465 starting at 38th and going north. You could look at some of those.
Inside of 465, you can drive north along Michigan road and find places, especially if you turn east on 71st (73rd?) and other roads, but you are on your own there.
If you are stubborn, you can tuck in around Georgetown between 16th and 38th, really 34th. Plan on daily carry, car break ins, and wrecks too.
Maybe I am getting old. When I was young I lived in some real low rent war zones in Atlanta, BUT my girl friend, now wife, did not live with me. She was in a better area. She was NEVER home alone at my apartment.