Romweber Marketplace is an antique mall inside of a former furniture factory. There are shops nearby the marketplace as well.
Trying Cincinnati-style chili is a must. Fortunately, there's one nearby!
Oldenburg is the german town just north of Batesville, which has a few shops and restaurants. The Pearl Street Pub is a family favorite restaurant, while Wagner's is a locally famous fried chicken establishment (James Beard American Classics Awarded). Oldenburg has a few antique and gift shops, as well as a dirndl shop. Importantly, the Holy Family Rummage Sale is taking place July 25-27. (https://holyfamilyoldenburg.com/events/rummage-sale/)
There's a few nearby state parks, including Versailles State Park (30 min drive) and Clifty Falls State Park (1 hr drive).
If you're interested in a day-trip, Madison Indiana (where Matt and Rachel are moving to) is roughly an hour away from Batesville. Madison has a lively historic district with shops, restaurants, and a riverfront park.
Cincinnati (~1 hr drive) has a well-known zoo, plenty of breweries and restaurants, a free art museum, a unique sign museum, among other things. The historic/downtown district is Over the Rhine (OTR). Ideas for half-day to full day activities are below: Rhinegeist (Matt and Rachel's favorite brewery): https://rhinegeist.com/ American Sign Museum: https://www.americansignmuseum.org/ Zoo: https://cincinnatizoo.org/ Aquarium: https://www.newportaquarium.com/ Art Museum: https://www.cincinnatiartmuseum.org/