Conil sits in one of the most interesting stretches of Andalucia, with several worthwhile destinations within an hour by car.
Vejer de la Frontera is 20 km inland and up on a hill: one of the most spectacular of the white towns, with a maze of narrow lanes, a Moorish castle, and views over the surrounding countryside. It is increasingly popular and somewhat gentrified, but still genuinely atmospheric. About 30 minutes by car.
The Cape of Trafalgar (Cabo de Trafalgar) is 15 km south — a windswept headland with a lighthouse and a long beach on the Atlantic side. The beach (Playa de los Caños de Meca) is one of the best on the coast: long, backed by pine trees and low dunes, and noticeably less crowded than Conil's main beaches. The cape is where the 1805 Battle of Trafalgar was fought, though there is nothing to see now except sea and sky.
Cádiz is 40 km north: a full city with significant monuments, a famous cathedral, good tapas, and an entirely different character from Conil. Worth a full day. Take the bus.
Tarifa, 60 km south, is Spain's wind-sports capital. The historic Moorish walls and the views to Morocco make it worthwhile even if you are not there to kitesurf.
The Parque Natural de la Breña y Marismas del Barbate extends south from Conil along the cliff coast to Barbate. It is excellent walking and birdwatching country — pine forest above the cliffs, salt marshes inland. The pinewood path between Barbate and Caños de Meca is one of the best coastal walks in Andalucia.