Morning: the old town, properly
Start at the castle — small, dense, and the one place the history stops being abstract. Then walk north into the lanes around Saripolou, which is where the city actually lives, and have coffee where the locals do rather than on the promenade.
Midday: Kourion
Nineteen kilometres west, and the single best thing in the district. The theatre is cut into the cliff with the sea straight below it, and the Eustolios mosaics are next to it. Two hours. Go before the afternoon heat.
Kolossi Castle is on the same road and takes an hour if you have it.
Afternoon: choose
Either the beach — Curium below the ruins, or Lady's Mile on the Akrotiri peninsula — or the hills. If you choose the hills, Lofou for the view and Omodos for the square.
You cannot do both. Anyone who tells you otherwise is selling you a tour.
Evening
Back to the marina for dinner, or the old port. And if you have had a bottle of Commandaria in a village at 4pm, this is the part of the day where having a driver stops being a luxury and starts being the plan.