Second tip if you want to discover Lindos without the crowds. Go on a Saturday, early in the morning or even late in the afternoon. Most all-inclusive hotels have their change over day so most people are flying out or into Rhodos.
I am sure you know about the fact that Rhodos is a bit ruined by these massive, all-in hotels, attracting tourists who are not the most pleasant to have. Even locals in Lindos shake their head when they talk about this kind of tourism and how it is ruining their island and lots of income for the Greek. For most independent travellers, Rhodes functions merely as a gateway to the smaller islands where you can still experience the real Greece. Like last time we discovered Tilos, Halki, Leros, Lipsi,…all reachable from the bigger islands like Rhodes and Kos but a world away from the gigantic all-inn resorts on these islands.
But back to Rhodes, that has its charm too of course. Believe me, on Saturday (at least in June) it’s more pleasant than on any other day in the week. Less bracelet-tourists and more locals in the small streets. You can almost imagine you are walking around in a chora from a small island.