  This paper discusses the ground state of quantum spins interacting via
Heisenberg antiferromagnetic exchange, in two dimensional lattices having
several different local environments. In unfrustrated lattices, when a N\'eel
type order exists, quantum fluctuations lead to an inhomogeneous order
parameter. I consider the effects of adding frustration to such a system by
including next nearest neighbor antiferromagnetic interactions. Within linear
spin wave theory, it is found that as the frustration parameter increases, the
local order parameters decrease at a rate that depends on the type of sites
involved in the frustrated loops. The examples of a decorated square lattice
system, and a quasiperiodic tiling are considered.
