We present a high spatial (diffraction-limited) resolution (~0.3") mid-infrared (MIR) spectroscopic study of the nuclei and star-forming regions of 4 local luminous infrared galaxies (LIRGs) using T-ReCS on the Gemini South telescope. We investigate the spatial variations of the features seen in the N-band spectra of LIRGs on scales of ~100 pc, which allow us to separate the AGN emission from that of the star formation (SF). We compare our Gemini T-ReCS nuclear and integrated spectra of LIRGs with those obtained with Spitzer IRS. The 9.7um silicate absorption feature is weaker in the nuclei of the LIRGs than in the surrounding regions. This is probably due to the either clumpy or compact environment of the central AGN or young, nuclear starburst. We find that the [NeII] luminosity surface density is tightly and directly correlated with that of Pa-alpha for the LIRG star-forming regions (slope of 1.00+-0.02). Although the 11.3um PAH feature shows also a trend with Pa-alpha, this is not common for all the regions. We also find that the [NeII]\Pa-alpha ratio does not depend on the Pa-alpha equivalent width (EW), i.e., on the age of the ionizing stellar populations, suggesting that, on the scales probed here, the [NeII] emission line is a good tracer of the SF activity in LIRGs. On the other hand, the 11.3um PAH\Pa-alpha ratio increases for smaller values of the Pa-alpha EW (increasing ages), indicating that the 11.3um PAH feature can also be excited by older stars than those responsible for the Pa-alpha emission. Additional high spatial resolution observations are essential to investigate, in a statistical way, the star formation in local LIRGs at the smallest scales and to probe ultimately whether they share the same physical properties as high-z LIRGs, ULIRGs and submillimiter galaxies.

23 pages (apjstyle), 19 figures, accepted for publicacion in ApJ