Context. Gaia data and stellar surveys open the way to the construction of detailed 3D maps of the Galactic interstellar (IS) dust based on the synthesis of star distances and extinctions. Dust maps are tools of broad use, also for Gaia-related Milky Way studies. Aims. Reliable extinction measurements require very accurate photometric calibrations. We show the first step of an iterative process linking 3D dust maps and photometric calibrations, and improving them simultaneously. Methods. Our previous 3D map of nearby IS dust was used to select low-reddening SDSS/APOGEE-DR14 red giants, and this database served for an empirical effective temperature- and metallicity-dependent photometric calibration in the Gaia G and 2MASS K_s bands. This calibration has been combined with Gaia G-band empirical extinction coefficients recently published, G, J, and K_s photometry and APOGEE atmospheric parameters to derive the extinction of a large fraction of the survey targets. Distances were estimated independently using isochrones and the magnitude-independent extinction K_J−Ks. This new dataset has been merged with the one used for the earlier version of dust map. A new Bayesian inversion of distance-extinction pairs has been performed to produce an updated 3D map. Results. We present several properties of the new map. A comparison with 2D dust emission reveals that all large dust shells seen in emission at middle and high latitudes are closer than 300 pc. The updated distribution constrains the well-debated, X-ray bright North Polar Spur to originate beyond 800 pc. We use the Orion region to illustrate additional details and distant clouds. On the large scale the map reveals a complex structure of the Local Arm. Chains of clouds of 2–3 kpc in length appear in planes tilted by ≃15° with respect to the Galactic plane. A series of cavities oriented along a l ≃ 60–240° axis crosses the Arm. Conclusions. The results illustrate the ongoing synergy between 3D mapping of IS dust and stellar calibrations in the context of Gaia. Dust maps provide prior foregrounds for future calibrations appropriate to different target characteristics or ranges of extinction, allowing us in turn to increase extinction data and produce more detailed and extended maps.