What’s “near,” 10 minutes, 15, 30, 60 . . . . And, do you mean for an RV, tent, or ???? Do you need/want: fishing, showers, a nearby town/city, a camp store, a campground or secluded spot, or ????
Can’t you give us more to work with?
Brown County SP is about 20 -25 minutes from I-65 (exiting at Columbus) while Spring Mill is more like 50 - 60 minutes from I-65 (exiting at Scottsburg). I'm sure you can find a good number of options between these two drive times and if you don't think the Spring Mill drive is too far and/or were willing to add a little to it (and consider the drive "close"), then you could add ever more options.
Would love to hear back from the OP about what is considered "close" (and other info),
Better ask when this poster means. Just so they aren't thinking about Memorial Day weekend.
The other major holiday weekends will also likely be either fully booked, or close to it.