Unrealized architecture is culturally significant. Although they remain imaginary, unrealized buildings happen to a community, often leaving unintended material and social traces. This article argues that unbuilt projects contribute actively to the production of locality and the meaning of neighborhoods and institutions. Drawing on theoretical investments from Appadurai and Yaneva, this article analyzes motifs of locality and globality in long-lasting controversies surrounding two unrealized Japanese-designed extension projects to European museum buildings: the Uffizi Gallery in Florence and the Institut Valencià d’Art Modern in Valencia. The analysis demonstrates that despite their spectacular confrontations, supporters and opponents in both cases shared similar notions of the affected neighborhoods and museums as meaningful social and cultural spaces. The controversies revolved around whether or not the Japanese-designed expansions would violate or reawaken perceived local energies and qualities. Engaging a little-studied dimension of cultural globalization, the article asks: what sort of locality emerges from unmaking globality-inflected monumental architecture?