If you choose to travel to Cadiz by plane, you can find flights to Jerez Airport, which is by far the closest option, or you can even fly to Sevilla which is only around an hour and a half away by car and train. Once at these airports you can take train or bus connections or rent a car to get to Cadiz.
If your flight arrives at the Jerez La Parra Airport, you can take the bus line M-050 Cadiz - Jerez - Airport which will take you straight to the centre of Cadiz. There is also a RENFE Cercanias train connection from the airport to the centre of Cadiz.
Further away is the airport in Seville, from where you can take the airport bus, which has frequent connections just outside arrivals and which will take you to the Santa Justa train station from which there are regular regional trains to Cadiz. You can also continue onto the El Prado bus station on the airport bus, from which you can catch a bus to Cadiz.
Another option, although rather more distant, is Malaga Airport where the bus line 19 will take you to the centre of Malaga, right next to the Maria Zambrano Train station. Here you can catch a train to Cadiz, although this route will require you to catch a connecting train in Seville or Dos Hermanas before reaching Cadiz.
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