  We report a detailed nuclear magnetic resonance (NMR) study by combined
$^{23}$Na and $^{75}$As measurements over a broad range of doping to map the
phase diagram of NaFe$_{1-x}$Co$_x$As. In the underdoped regime ($x \le$
0.017), we find a magnetic phase with robust antiferromagnetic (AFM) order,
which we denote the {\it s}-AFM phase, cohabiting with a phase of weak and
possibly proximity-induced AFM order ({\it w}-AFM) whose volume fraction $V
\simeq 8$\% is approximately constant. Near optimal doping, at $x = 0.0175$, we
observe a phase separation between static antiferromagnetism related to the
{\it s}-AFM phase and a paramagnetic (PM) phase related to {\it w}-AFM. The
volume fraction of AFM phase increases upon cooling, but both the N{\'e}el
temperature and the volume fraction can be suppressed systematically by
applying a $c$-axis magnetic field. On cooling below $T_c$, superconductivity
occupies the PM region and its volume fraction grows at the expense of the AFM
phase, demonstrating a phase separation of the two types of order based on
volume exclusion. At higher dopings, static antiferromagnetism and even
critical AFM fluctuations are completely suppressed by superconductivity. Thus
the phase diagram we establish contains two distinct types of phase separation
and reflects a strong competition between AFM and superconducting phases both
in real space and in momentum space. We suggest that both this strict mutual
exclusion and the robustness of superconductivity against magnetism are
consequences of the extreme two-dimensionality of NaFeAs.
