1H NMR of 4-Methylanisole
The methoxy group actually interacts with the aromatic ring via two competing mechanisms. 

It is indeed electron withdrawing via the sigma bond interaction between the O and C of the aromatic ring. However the lone pair on the oxygen conjugates through the delocalised pi network and increases the electron density at both the ortho and para positions. If you draw out the conjugation pathway you will see the electrons can sit on the ortho and para carbons. This is the more significant contributor to the overall electronics and, therefore, chemical shift. So, the protons ortho to methoxy are far more shielded than those ortho to the weakly electron donating methyl group. 

This effect can be generalised across all aromatic directing groups, and the size of chemical shift difference from benzene (7.3ppm) is directly correlated to the strength of the directing group. So, aniline has ortho chemical shift of about 6.5ppm (-NH2 is a strong EDG), while the ortho protons in nitro benzene are up at about 8.5ppm (-NO2 is a strong EWG).