There are plenty of nice places in the downtown area within four to five blocks of the circle. Getting further out gets you in some ok , but not awesome areas. Over by the airport is kind of what you would expect and I'd steer clear of there , though it's not horrible.

It's really how close to the circle you want or need to be and what do you want to spend?

If you have a full day of downtime available, consider:
- Going to the USAF Museum in Dayton, OH - it's about a 2-hour drive on I-70 East and is well worth the trip. Plan on 6 to 8 hours or so to 'fast-track' through most of the museum. https://www.nationalmuseum.af.mil

- If you have 2 full days available back-to-back, go from the USAF Museum south to Kings Island (45 minute to 1 hour drive) toward Cincinnati and spend a day there. Fun amusement & water park. Easy drive back to Indy on I-74, roughly 2 hours. You could also make this a single day trip. https://www.visitkingsisland.com

If you or the kids have an interest in racing:
Indianapolis Motor Speedway Museum https://imsmuseum.org

@mag162

Avoid the area inside I-465.

The Indiana War Memorial Museum is in downtown Indianapolis & it's free.  It's very cool & is really well done.  I would also suggest the Indianapolis Zoo and depending on the age of your kids the Children's Museum.  Downtown Indy is pretty safe but like every other major city it has a problem with homeless people, but unlike other cities they aren't allowed set up camps downtown.

You're may not want to be downtown on friday and saturday nights during the Indiana Black expo. Traffic will be gridlocked, Im not sure if the shootings are the same as years past but I cant imagine its slowed down.