We examine several point processes associated with solid-state nucleation and growth scenarios in which nucleation sites are uniformly distributed on subspaces in ${ℝ}^2$. Such nucleation scenarios model, for example, phase formation in the presence of exclusion zones, on internal interfaces (e.g., grain boundaries) and on grain triple junctions. Some of these processes are shown to exhibit anti-hyperuniformity with respect to point numbers that reflects underlying site clustering, and this behavior is described in terms of geometrical models that capture the dependence of the associated structure factor on wavenumber in the limit of small wavenumber. The resulting coalesced microstructures whose grains emanate from nucleation sites are then analyzed using spectral graph theory, and a link is established between anti-hyperuniform behavior and key eigenvalues in the spectrum of a Laplacian operator on these networks.