I’m not sure if you intend to lodge in Cádiz or another town. If Cádiz, then I’ll suggest the Parador. If someplace else, we enjoyed our stay at Hotel Duque de Nájera in Rota a number of years ago. Both hotels have onsite parking. There is a ferry that runs from the pier by the Duque over to Cádiz if you didn’t want to drive it..
There are no wow sites along the Costa de la Luz, but there are plenty of beaches. April is slightly before the main tourist season so the crowds won’t be bad.
There is a small castle in Puerto de Santa María where Ferdinand and Isabella supposedly gave Columbus the money for one of his voyages. Jerez de la Frontera is always a place to visit with its Alcazaba, Sherry bodegas, and equestrian center. Near San!úcar de la Barrameda is a bird observation area if you’re into that. There’s a castle ruin in Medina-Sidonia. Along the coast are a few small towns worth short visits. If you enjoy windsurfing or watching it, near Tarifa is Punta Paloma. The drive from Cádiz to Tarifa should take less than 1.5 hours without stops.