We examine star formation activity in a distant (z < 0.1) and flux-limited sample of quasars (QSOs). Midinfrared (MIR) spectral diagnostics at high spatial resolution (∼0.4 arcsec) yield star formation rates (SFRs) in the inner regions (∼300 pc-1 kpc) for 13 of 20 of the sample members. We group these objects according to the size probed by the high angular resolution spectroscopy, with characteristic scales of <0.7 and ∼0.7-1 kpc. Using the polycyclic aromatic hydrocarbon (PAH) feature at 11.3 μm, we measure SFRs around 0.2 and 1.6 M ⊙ yr-1. We also measure the larger aperture PAH-derived SFRs in the individual IRS/Spitzer spectra of the sample and obtain a clear detection in ∼58% of them. We compare smaller and larger aperture measurements and find that they are similar, suggesting that star formation activity in these QSOs is more centrally concentrated, with the inner region (≲1 kpc) accounting for the majority of star formation measured on these scales, and that PAH molecules can be present in most local MIR-bright QSOs within a few hundred parsecs from the central engine. By comparison with merger simulations, we find that our estimation of the SFR and black hole (BH) accretion rates are consistent with a scenario in which the star formation activity is centrally peaked as predicted by simulations.