No country lies directly across from Panama City Beach, Florida. The beach faces south onto the Gulf of Mexico.
The Gulf of Mexico is a semi-enclosed basin bordered by the US (north), Mexico (west/south), and Cuba (southeast). Panama City Beach looks out over the northeastern Gulf—open water to the horizon.
People sometimes confuse "Panama City Beach" (Florida) with "Panama City" (Panama, on the Pacific). The latter does face the Pacific Ocean.