For the most part it is safe. Use normal common sense for visiting big cities. Homeless people are often pan handling on the streets and can be a little pushy in the downtown area. I wouldn't walk alone at night. They also increase police presence during these events. You will see them on bikes and horses.
Indianapolis is fairly safe, during the day. I was just there in January at 11PM. I was in the Market Area. Unfortunately they have seen an influx of Chicago, as has Michigan. It is a great place to visit.
