  $^{115}$In Nuclear magnetic resonance data are presented for a series of
Ce$_{1-x}$La$_x$CoIn$_5$ crystals with different La dilutions, $x$. Multiple
In(1) sites associated with different numbers of nearest-neighbor cerium atoms
exhibit different Knight shifts and spin lattice relaxation rates. Analysis of
the temperature dependence of these sites reveals both an evolution of the
heavy electron coherence as a function of dilution, as well as spatial
inhomogeneity associated with a complete suppression of antiferromagnetic
fluctuations in the vicinity of the La sites. Quantum critical fluctuations
persist within disconnected Ce clusters with dilution levels up to 75%, despite
the fact that specific heat shows Fermi liquid behavior in dilute samples.
