good luck finding a place in a hostal on those dates, as Cadiz will be in full blown carnaval mode; that said you probably wont have any problems sleeping out on the beach, pitch a tent and you may get a visit from the policia local. Another possibility could be going further away from the city into the "costadura", the beaches on the outskirts towards san fernando, its a lot more remote and you'll have it more or less to yourself, but I am not suggesting you do this....enjoy carnaval at any rate