The port area isn't huge so you should dock within walking distance of the train station. The train will quickly take you to San Fernando station from which a footpath (Sendero Salina Dolores) takes you along the edge of the salinas back towards Cadiz. I've not done the walk personally but you should pick up a few species. Alternatively, walk (or better still take a taxi) from the station for c3 km to a much better site, the Sendero Tres Amigos, which takes you into the salinas where you should find a variety of waders, Flamingos, Auduoin's Gull, Spoonbill, etc. You should also be able to catch a bus to the university campus and walk through the pines, across a foot bridge to the Valdegrama area. Ferries over to El Puerto can be fun too. For local buses see
http://siu.cmtbc.es/es/lineas.php However, I would advise you to contact a local guide who could pick you up and allow you to get to more interesting sites by car which would open up the possibility of species like Crested Coot, White-headed Duck, etc. I should be in Spain in early April and would have been happy to take you out myself but I'm with friends so can't volunteer them as well. Send me a PM with your email and I'll send my detailed notes on birding in the area which should give you some ideas.