It really depends on your choice of leisure activities - for example, downtown Indy is safe and is convenient for bars, nightclubs, theater, etc. - but rentals are a little more expensive than other areas. A recent survey of crime in the county revealed the safest areas to be the extreme south and northwest sections of Marion County - basically suburbs.
If you have children, the answer would be different. In that case, I would suggest Hamilton County (to the north), or Johnson County (to the south). That opinion is based on school performance.