I understand you are going on foot, right?
You have the so called "camino del estrecho". All I can say is, Cádiz is a blessed place on Earth.
I have seen some very vague information here
EN CONSTRUCCIÓN Nos consta que son muchas las personas que han intentado peregrinar hasta el Finisterræ desde lo que se ha dado en llamar la “Punta de Europa”; desde las «Columnas de Hércules» hasta las cercanías de la «Torre de Hércules», desde la Costa de la Luz hasta las proximidades de la...
www.mundicamino.com
I believe it is called "Camino del Estrecho". I know a few stretches, but I would use "wikiloc.com" for more accurate reference.
Algeciras-Tarifa
you can go all the way along the coast, I believe, but if you discover the cork oak mountain forests with holly, ferns and rain forests you would be shocked. I would go over Botafuego to Garganta del Capitán, Las Corzas, the youth hostel Inturjoven in El Bujeo, then down to the coast and follow the stunning coast to Tarifa along the Flysch geological rocks, with Africa just at a stone throw, over Guadalmesí river and onto Tarifa.
Tarifa - Bolonia
is a stretch you can do walking on the beach, you will find some bar open along the way, thousands of surfers and the cleanest sand in the world. You might find some rocky outcrops much easier to manage on low tide (and good waves). In Bolonia you will find restaurants, bars and some amazing Roman ruins.
Bolonia-Zahara de los Atunes
you can climb the massive dune west of Bolonia and walk along the beach, the cliffs, the Cañuelo forest and beach, up the lighthouse of Camarinal, the posh Alemanes cove, Atlanterra residential area, then 4 km of pristine beach.
I believe from Bolonia onwards there is another variant that goes over Facinas and the Janda flats.
Zahara de los Atunes - Barbate
Along the beach again, some 8 km along virgin beaches, to Barbate. No bars along the beach, though, in fact it is a military area and might be banned to public access at rare teams
Barbate-Los caños de Meca
Past Barbate, a fabulous walk among pine trees over mid height cliffs.
Los Caños-Trafalgar-Zahora-Conil
Pure beach walk, sandy all the way, a couple of bars along the way. Conil is a nice little town
Conil - Chiclana
Cliffs, pine tree forest, no more beach walk.
Chiclana -Sancti Petri-Cadiz
pine trees, no more beach walk too many cliffs, and lots of tarmac as you approach the jewel that Cadiz city is.