On a budget, Akrotiri Archaeological Site still earns its price.
~€12 entry (or via combined ticket)
Often called the 'Greek Pompeii,' Akrotiri is genuinely extraordinary: you walk among 3,600-year-old streets and houses preserved in volcanic ash, sheltered and shaded. The catch is that the famous frescoes are in museums elsewhere and casual visitors may find the ruins abstract without a guide or audio. For anyone curious about history it's the island's most substantial sight.