Jori’s answer does a nice job in explaining why aromatic rings generally shift proton shifts downfield, and why this is not restricted to the aromatic protons themselves; see the pictures at the beginning of his post for explanation (and replace the benzene proton with a $\ce{CH2}$ group in the right-hand side picture for further clarity).
The difference in chemical shift $\Delta \delta(\ce{C\mathbf{H}_2OH}) = 0.47~\mathrm{ppm}$ which is a very small, almost neglegible difference. Compare:
the difference between naphthalene-1-ylmethanol and benzyl alcohol: $\Delta \delta(\ce{C\mathbf{H}_2OH}) = 0.41~\mathrm{ppm}$
the difference between benzyl alcohol and methanol: $\Delta \delta(\ce{C\mathbf{H}_{$n$}OH}) = 1.12~\mathrm{ppm}$
(Note that we cannot strictly compare the chemical shift difference between naphthalene-1-ylmethanol and anthracene-9-ylmethanol since the latter has been measured in $\ce{(CD3)2SO}$ rather than $\ce{CDCl3}$. However, the general trend works)
The big difference in shifts occur when we add an aromatic ring to our methyl alcohol; the number of six-membered aromatic rings does not really matter. This is because the first ring is added in close vicinity to the centre in question while the other rings are further away — we might compare this to the difference in chemical shifts between ethanol and 2-phenylethanol: $\Delta \delta (\ce{C\mathbf{H}_2OH}) = 0.09~\mathrm{ppm}$ (even smaller). However, this last comparison is not strictly valid due to the flexibility of 2-phenylethanol being larger than that of the polyaromatic systems.
Summed up in a nutshell: The chemical shift difference between naphthalene-1-ylmethanol and anthracene-9-ylmethanol can be attributed to the presence of a third aromatic ring in relative proximity of the group in question.
Your second (unrelated, and probably should have been posted separately) question deals with how groups outside of a phenyl ring influence the chemical shifts of protons belonging to that ring.
In the case of benzil, we are dealing with an electron-withdrawing carbonyl group, and we might as well choose the simpler benzaldehyde system for comparison. You can picture the electron-withdrawing effect of the carbonyl group by a set of enolate resonance structures including charge separation: We can relocate the positive charge to the ortho- and para-positions of the phenyl ring, but not to the meta-positions, resulting in a lower electron density at ortho and para and thus greater deshielding and a downfield shift.
Similarly for electron-donating groups such as the methoxy group in anisole: The ortho- and para-positions are shifted upfield because the electron-donating group supplies their positions with a greater electron density and thus more shielding. The meta-groups are rather unaffected by that.
This can be generalised to the (not necessarily always true!) statement:
Groups in benzylic positions generally leave meta-positions unaffected and affect mainly the chemical shifts of ortho- and para-positions.
Therefore we expect a downfield shift for ortho- and para-protons in benzil and no shift change for the meta ones.