United and Lufthansa have round-trip flights from Houston (IAH) to Zagreb (ZAG) for $507-$593 with a connection. Flights in March, October, November, and December. Departures on Tuesday, and Wednesday. Flight may operate as a Croatia Airline flight.
Note: The Lufthansa fares for $507 are “Basic Economy” with a very bad carry-on weight allowance of 18-lbs, and no checked bags. The United fares for $593 are “Real” Economy. Which allows for a free carry-on and checked-bag, 50-lbs each.