  We report measurements of the first-flux-penetration field in surface-treated
and coated Nb samples using muon spin rotation ($\mu$SR). Using thin Ag foils
as energy moderators for the implanted muon spin-probes, we "profile" the
vortex penetration field $\mu_{0} H_{\mathrm{vp}}$ at sub-surface depths on the
order of $\sim 10$ $\mathrm{\mu}$m to $\sim 100$ $\mathrm{\mu}$m. In a coated
sample [Nb$_3$Sn(2 $\mathrm{\mu}$m)/Nb], we find that $\mu_{0} H_{\mathrm{vp}}$
is depth-independent with a value of 234.5(35) mT, consistent with Nb's
metastable superheating field and suggestive of surface energy barrier for flux
penetration. Conversely, in a surface-treated sample [Nb baked in vacuum at 120
$^{\circ}$C for 48 h], vortex penetration onsets close to pure Nb's lower
critical field $\mu_{0}H_\mathrm{c1} \approx 170$ mT, but increases with
increasing implantation depth, consistent with flux-pinning localized at the
surface. The implication of these results for technical applications of
superconducting Nb, such as superconducting radio frequency (SRF) cavities, is
discussed.
