West side is the river, although with the improvements along the west side of the river it makes for good biking and jogging. East side is I-65/70, gets dodgy past that very quickly. There are exceptions of course but most of the areas past those boundaries still face issues.
Inside those boundaries though, like from Mass Ave/Lockerbie/Chattham Arch over to IUPUI/White River park, everything is normally very safe. I'm not thrilled with my wife jogging just anywhere after dark, but it can be done.
The bigger issue as someone mentioned, is that compared to some cities Indy is just totally dead in most places. If you get to Mass Ave or if you are on Illinois by the mall area, there are plenty of people. But walk from Hoaglins to the canal on a Sunday and you might pass 10 people total.
We've never understood why because there are tons of homes/condos downtown. There are a lot more places to live now than there were 10 years ago. But the pedestrian traffic hasn't seemed to pick up.