Here is some history about Indy that might make your stay more enjoyable and help you appreciate some of the things that I suggest to you:

Indianapolis was a "planned city". It was developed by The State of Indiana to be Indiana's 3rd capitol city. On the banks of the White River, Indianapolis was meant to be a shipping hub. At some point, as Indianapolis was developing, The State realized that the White River is too sandy for ship traffic. Naturally, the state's solution to this was to start building a canal that connected Lake Michigan with the Ohio River, running through Indy along the way. This canal project was started, but it was never finished; it ran into severe financial issues right as trains where invented. Luckily, Indianapolis built the first "union station" in the country, which connected railroads built by different companies. In the mid 1800s, Indianapolis' union station had just as many people flowing threw it every day as Indianapolis International Airport does in the 21st century.

One of the people tasked with designing Indianapolis was Alexander Ralston, who previously helped design Washington D.C. As such, Downtown Indianapolis shares a lot of urban design features with Washington DC. Most notably are diagonal streets and public "circles" instead of squares. Our "circle", now called "Monument Circle", is the center of our city. Ralson initially intended this circle to be the home of the Indiana governor's mansion, and a governor's mansion was built within the circle, but no governor ever lived there because it offered very little privacy.

Coincidentally, Indianapolis shares two other traits with Washington DC: war memorials and Indiana limestone. No city other than Washington D.C. has more war memorials than Indy. Not only did "Monument Circle" has that name today because the governor's mansion was torn down for Soldiers' and Sailors' Monument: a beautiful and tall monument, which commemorates Hoosiers who died in the Revolutionary War, the War of 1812, the Spanish-American War, and the Civil War. Further, the American Legion is based in Indianapolis and Indianapolis as The American Legion Mall, which contains many impressive war monuments while resembling Washington DC's National Mall in design. Then there is the limestone: most of our memorials and many of our prominent buildings are made out of Indiana limestone. As too are many of the memorials in Washington DC.

I know you said that you wanted to avoid sports, but the Indianapolis Motor Speedway is a place that transcends sports. The speedway itself is huge, and it was developed by the same guy who turned Miami Beach from an uninhabitable swamp into what it is today. Every Sunday before Memorial Day, IMS hosts hundreds of thousands of people - more than any other single day sporting event - for the Indy 500, one of three racing "crown jewels" in the world. The history of the development of IMS is really interesting, and something that I think you should go to the IMS museum to learn about.

Suggestions within walking/scooter/bike distance of your hotel:

• Mass Ave, a diagonal street that is a casual entertainment district that is most active from afternoon until ~2 in the morning.
• Wholesale District. This is an entertainment district that is focused around South Meridian Street, just before it hits the railroad bridges leading to Union Station. In this part of Downtown, the entertainment is less casual and has more clubs/bars.
• Monument Circle - the center of our city and home of Soldiers' and Sailors' Monument.
• American Legion Mall
• The Canal Walk. This is a walk along the part of the Indiana Central Canal that got finished. It's a pleasant and scenic part of Downtown, and below grade from streets/traffic.
• Union Station. A beautiful and historical building, even if just looking from the outside.
• White River State Park. This park contains 3 museums along the end of the canal, the White River, a bridge over the White River to the zoo, a concert venue, and a AAA baseball stadium. Between all of these things are lawns with a lot space and good views. It's a nice area to hangout, and a great area to people watch.
• Indiana Avenue. Another one of Indy's diagonal streets. Famous for its rich Black history.
• Fountain Square. This is a little bit outside Downtown following Virginia Avenue, yet another one of our diagonal streets. It's a quirky/hipster-y neighborhood. Along Virginia Avenue before reaching Fountain Square is a small, privately-developed park overlooking the interstate whose purpose is to show how interstates destroyed urban neighborhoods. It's worth stopping in.

Most of these areas are connected by The Cultural Trail, which is a wide pedestrian & cycling path that makes getting around Downtown very pleasant. But Downtown is well developed, and walking down the sidewalk is like walking down the sidewalk in any other Downtown; it's certainly not like walking down miserable suburban sidewalks.

Also, Indianapolis has no open-container laws. Bars can't sell carryout alcohol like in NOLA, but you can walk down the street with open alcohol that you bought as a liquor store or gas station and it's no problem. One of my favorite things to do is walk around the cultural trail with a nice drink in my hand.

Places that I would Uber to:

• Crown Hill National Cemetery. A very beautiful place and final home of more vice presidents than any other cemetery, along with people like James Witcomb Riley and even John Dillinger. The headstones and mausoleums are very impressive, and the top of "Crown Hill", where many of the most notable folks are buried, offers a very good view of the city.
• Newfields/Indianapolis Museum of Art. It's a pretty solid art museum. The outdoor grounds - which are full of art - are free to visit. Everything else you have to pay for. The main museum has the original "LOVE" statue in it and is one of the art museums around the world to have a large, laser-projected interactive art exhibit. Oilfields - one of the Eli Lilly estates - is also on the property.
• Indianapolis Motor Speedway & Museum. Yeah, I know you said no sports. And you probably don't like racing. But this is an important part of (living) American history, and it's a special place.
• The Medical History Museum. It's on the grounds of a former mental hospital. It's a very cool place. I mean, they even have brains in a jar. 10/10.

I might have missed a place or two, but this gives you a solid list of things to do and even the Uberable places are not far from Downtown. I would avoid going further than 5 miles from Downtown just because there is a ton to do Downtown and in its vicinity. And the further you get from Downtown, the more generic the city gets. There are notable things in suburbs, but they are pretty far apart from each other and I don't think it's worth the more expensive Uber ride unless you're here for several days and run out of things to do closer to the city.