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We present new millimeter and infrared spectroscopic observations towards theradio nebula G10.0-0.3, which is powered by the wind of the Luminous BlueVariable star LBV 1806-20, also closely associated with the soft gamma-rayrepeater SGR 1806-20, and believed to be located in the giant Galactic HIIcomplex W31. Based on observations of CO emission lines and NH_3 absorptionfeatures from molecular clouds along the line of sight to G10.0-0.3, as well asthe radial velocity and optical extinction of the star powering the nebula, wedetermine its distance to be 15.1$^{+1.8}_{-1.3}$ kpc in agreement with Corbelet al. (1997). In addition, this strengthens the association of SGR 1806-20with a massive molecular cloud at the same distance. All soft gamma-rayrepeaters with precise location are now found to be associated with a site ofmassive star formation or molecular cloud. We also show that W31 consists of atleast two distinct components along the line of sight. We suggest thatG10.2-0.3 and G10.6-0.4 are located on the -30 km/s spiral arm at a distancefrom the Sun of 4.5 $\pm$ 0.6 kpc and that G10.3-0.1 may be associated with amassive molecular cloud at the same distance as the LBV star, i.e.15.1$^{+1.8}_{-1.3}$ kpc, implying that W31 could be decomposed into twocomponents along the line of sight.Comment: Accepted for publication in Astronomy & Astrophysics (12 pages

The connection between W31, SGR 1806–20, and LBV 1806–20: Distance, extinction, and structure