we aim to characterize the properties of the stellar populations in the central few hundred parsecs of nearby galactic nuclei: age, mass, and 3D geometry. We use spatially resolved spectroscopic observations of NGC 1433, NGC 1566 and NGC 1808 obtained with SINFONI to constrain a 3D model composed of a spherically symmetric Nuclear Star Cluster (NSC) and an extended thick stellar disk. We computed UV to Mid-Infrared Single Stellar Population (UMISSP) spectra to determine the age of the stellar populations and construct synthetic observations for our model. To overcome usual degeneracies between key parameters, we simultaneously fit the spatially resolved line-of-sight-velocity, line-of-sight-velocity-dispersion, low spectral resolution NIR continuum and high spectral resolution CO absorption features for each pixel. For the three objects, we derive the age and mass of the young and old stellar populations in the NSC and surrounding disk, as well as their 3D geometry: radius for the NSC; thickness, inclination and position angle for the disk. These results are consistent with published independent measurements when available. Conclusions. The proposed method allows to derive a consistent 3D model of the stellar populations in nearby galactic centers solely based on a NIR IFU observation.