Solo, Caldera Rim Viewpoints works.
The caldera is the whole reason Santorini looks the way it does, and standing at the edge looking 300m down to the water is the single best free thing on the island. The honest catch is that 'the viewpoint' isn't one place — the best ones are simply wherever you're standing on the rim, and the famous spots get mobbed. Pick a quiet stretch and it's pure.