I grew up in Cincinnati, my sister lives in Cincinnati, and I've traveled there in my Model 3 several times, so I know something about the geography of the area but less about Supercharger placement. (I have charged at the
Cincinnati Supercharger location, though.)
Batavia is significantly to the east of Cincinnati proper; Google Maps says it's a 29-mile drive from there to my sister's house in Clifton, for instance; or 17 miles from there to the Cincinnati Supercharger. According to PlugShare, there are three Superchargers in the Cincinnati area, but they're all clustered much more closely around the main Cincinnati urban area, not as far into the suburbs/exurbs as Batavia.
Tesla's strategy for Supercharger placement has mainly been to support inter-city travel, and secondarily to support Tesla owners who need to charge closer to home. Batavia isn't located on a major highway between Cincinnati and anywhere else, so it's not a prime location for the first goal; and it's too far into less-populated areas to make it a good location for Supercharger placement for the second goal. You'll find a
lot of places in the US that are farther from a Supercharger than Batavia.
That said, Batavia seems to have next to nothing in non-Tesla DC fast charging or even in Level 2 charging, too. The closest seems to be a
Duke Energy Level 2 station. There's also a
campground with a NEMA 14-50 plug. This isn't a Tesla-specific issue; we as a society need to build out more and better EV charging infrastructure. As a practical matter, depending on where you were staying, you might be able to plug into a 120v or maybe 240v outlet wherever you were staying, If 120v, that won't charge you quickly, but if you were staying for a day or more, it would help. Planning ahead and charging at whatever Supercharger was closest when heading in to the destination would also help.
The good news, of course, is that this is all improving; every company involved in EV charging, including Tesla, is building out more infrastructure. We're still a ways from having as much EV charging infrastructure as there is gasoline fueling infrastructure, though.
