  Aims. We aim to characterize the properties of the stellar populations in the
central few hundred parsecs of nearby galactic nuclei; specifically their age,
mass, and 3D geometry. Methods. 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
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. Results. 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 us to derive a consistent 3D model of the stellar populations in
nearby galactic centers solely based on a near-infrared IFU observation.
