The old town and the main beaches are walkable from each other. Conil is small enough that you rarely need transport within the core area — the centro and Playa de los Bateles are ten minutes apart on foot.
For the northern beaches, particularly Cala del Aceite and the coves beyond it, a bicycle or car makes a real difference. Bike rental shops operate along the beach road in summer. The paths north along the coast are mostly flat with a few short climbs at the headlands.
Local buses run in summer between the town centre and some of the more distant beaches, including El Palmar, but services are infrequent outside peak season. Check current timetables on arrival.
Taxis are available from the rank near the bus stop on Avenida de la Playa. In July and August the waits can be long; it's worth getting the number of a local taxi company.
A car is genuinely useful for day trips to Vejer de la Frontera, the Cape of Trafalgar, and the inland white towns. Parking in the centre in summer is miserable — most people park on the periphery and walk.