We use Type Ia supernovae (SNe Ia) discovered by the Sloan Digital Sky Survey-II SN Survey to search for dependencies between SN Ia properties and the projected distance to the host-galaxy center, using the distance as a proxy for local galaxy properties (local star formation rate, local metallicity, etc.). The sample consists of almost 200 spectroscopically or photometrically confirmed SNe Ia at redshifts below 0.25. The sample is split into two groups depending on the morphology of the host galaxy. We fit light curves using both MLCS2k2 and SALT2, and determine color (A(V), c) and light-curve shape (Delta, x(1)) parameters for each SN Ia, as well as its residual in the Hubble diagram. We then correlate these parameters with both the physical and the normalized distances to the center of the host galaxy and look for trends in the mean values and scatters of these parameters with increasing distance. The most significant (at the 4 sigma level) finding is that the average fitted A(V) from MLCS2k2 and c from SALT2 decrease with the projected distance for SNe Ia in spiral galaxies. We also find indications that supernovae (SNe) in elliptical galaxies tend to have narrower light curves if they explode at larger distances, although this may be due to selection effects in our sample. We do not find strong correlations between the residuals of the distance moduli with respect to the Hubble flow and the galactocentric distances, which indicates a limited correlation between SN magnitudes after standardization and local host metallicity.