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Aims. 3D tomography of the interstellar dust and gas may be useful in many respects, from the physical and chemical evolution of the interstellar medium itself to foreground decontamination of the cosmic microwave background, or various studies of the environments of specific objects. However, while spectral data cubes of the galactic emission become increasingly precise, the information on the distance to the emitting regions has not progressed as well and relies essentially on the galactic rotation curve. Our goal here is to bring more precise information on the distance to nearby interstellar dust and gas clouds within 250 pc. Methods. We apply the best available calibration methods to a carefully screened set of stellar Strmgren photometry data for targets possessing a Hipparcos parallax and spectral type classification. We combine the derived interstellar extinctions and the parallax distances for about 6000 stars to build a 3D tomography of the local dust. We use an inversion method based on a regularized Bayesian approach and a least squares criterion, optimized for this specific data set. We apply the same inversion technique to a totally independent set of neutral sodium absorption data available for about 1700 target stars. Results. We obtain 3D maps of the opacity and the distance to the main dust-bearing clouds within 250 pc and identify in those maps well-known dark clouds and high galactic more diffuse entities. We calculate the integrated extinction between the Sun and the cube boundary and compare this with the total galactic extinction derived from infrared 2D maps. The two quantities reach similar values at high latitudes, as expected if the local dust content is satisfyingly reproduced and the dust is closer than 250 pc. Those maps show a larger high latitude dust opacity in the North compared to the South, reinforcing earlier evidences. Interestingly the gas maps do not show the same asymmetry, suggesting a polar asymmetry of the dust to gas ratio at small distances. We compare the opacity distribution with the 3D distribution of interstellar neutral sodium resulting from the inversion of sodium columns. We discuss the similarities and discrepancies and the influence of data set limitations. Finally we discuss the potential improvements of those 3D maps.