<map lat='36.50170224572221' lng='-6.269159317016602' zoom='14' view='2' float='right' /> Cádiz is a city and port in southwestern Spain. It is the capital of the Cadiz Province and also the oldest continuously-inhabited city in the Iberian Peninsula and possibly of all southwestern Europe.
Walk down along the street Avenida de Cayetano del Toro until the last petrol station (on your right) before the N-443 and CA-33 split. Ask people (learn some Spanish) and/or use signs.
EDIT: Petrol station mentioned above (Repsol) is good for Tarifa/Gibraltar as most of the traffic to Sevilla/Jerez sticks to the left line to turn into N-443 road. Walk another 5-10min along that road (viaduct) and on your right hand side you will have Cepsa petrol station. The traffic there is a bit smaller, but it has plenty of space for the cars to stop and all the heavy traffic from Cadiz port pass through there. http://hitchwiki.org/maps/?zoom=16&lat=36.495714941084344&lon=-6.2632015943526245
South (with a ferry)
Trucks are allowed to take one person + driver. Hitching to e.g. Las Palmas should be possible (untested).
The port office claims that that most of the private sailing boats to Canary Islands leave between January February and then again from June/July until November, due to wind conditions. However, there are anecdotal accounts that boat hitchhiking is possible to the Canary Islands and the Americas.
In spring, there are always some people sleeping at the Caleta beach in tents, but in summer it may be unsafe as there are too many people around. The beaches further down the coast are way more quiet, but it takes at least half an hour to get there on foot from the old part of the city.