Looks like I can fly BA from Cinci to Zagreb with one stop in London. Not too bad. Might end up being the option. Curious if there are any nonstop flights from Midwest or east coast in US to anywhere in Croatia? It looks like maybe during the summer on United out of Newark?
matrix.itasoftware.com can show you flight schedules, and you can
specify non-stop as one search parameter.
You might look at the airport sites for Zagreb, Split, and Dubrovnik for
other non-stop possibilities.
Zagreb has a smallish airport. There are no direct flights currently between Zagreb and the United States. You will need to transit somewhere.
One thing I often do is check the airport wiki page to see what cities are served. For example, Zagreb doesn’t show any flights to the U.S (scroll down to ”Airlines and Destinations” on the page)
https://en.wikipedia.org/wiki/Zagreb_Airport
Dubrovnik shows a seasonal flight on United:
https://en.wikipedia.org/wiki/Dubrovnik_Airport