We study vortex-lattice phases for a Bose gas trapped in a rotating optical-lattice near the superfluid-Mott-insulator transition. We find a series of abrupt structural phase transitions where vortices are pinned with their cores only on plaquettes or only on sites. We discuss connections between these vortex structures and the Hofstadter-butterfly spectrum of free particles on a rotating lattice. © 2008 The American Physical Society.