R114
PHB p.204: "A typical spell requires you to pick one or more targets[:] creatures, objects, or a point of origin", so the caster decides where the area originates. Later in the same section, the language is repeated: "You select a cube's point of origin", "You select a sphere's point of origin", etc. Further guidance for placing an AoE on a grid can be found on DMG p.251 and XGE p.86, where it appears the implicit suggestion is to pick a point on the edge of a token.