How late r ya considering? It has a bearing re location on Rhodes n maybe weather wise! Rhodes has a long, long season extending well into Oct but it is a fact that Lindos/Pefkos/Lardos in the South East experience the better weather later into the season.
Pefkos would b good if you r seeking good beaches, good bars n great restaurants. The beaches continue as far as Lardos 3km away and u can walk all the way, Ive done it a few times. Pefkos is a purpose built resort with no authentic Greek atmosphere but it attracts families n couples alike.
Lindos is unique, it enjoys world heritage status, has a fantastic choice of roof top restaurants with unrivalled views. It also has a great range of bars which stay open until the very early hours. The beaches and the bays are better than Pefkos and if it is walks u like, I often do the 'tomb walk' which takes u from the village to the headland looking back at Lindos, perfect photo opportunity. However, Lindos is swamped with day trippers between 10am n 4pm and is hilly so not so good if anyone has mobility issues.
Yr call, depends what u r looking for!