  We present new millimeter and infrared spectroscopic observations towards the
radio nebula G10.0-0.3, which is powered by the wind of the Luminous Blue
Variable star LBV 1806-20, also closely associated with the soft gamma-ray
repeater SGR 1806-20, and believed to be located in the giant Galactic HII
complex W31. Based on observations of CO emission lines and NH_3 absorption
features from molecular clouds along the line of sight to G10.0-0.3, as well as
the radial velocity and optical extinction of the star powering the nebula, we
determine its distance to be 15.1$^{+1.8}_{-1.3}$ kpc in agreement with Corbel
et al. (1997). In addition, this strengthens the association of SGR 1806-20
with a massive molecular cloud at the same distance. All soft gamma-ray
repeaters with precise location are now found to be associated with a site of
massive star formation or molecular cloud. We also show that W31 consists of at
least two distinct components along the line of sight. We suggest that
G10.2-0.3 and G10.6-0.4 are located on the -30 km/s spiral arm at a distance
from the Sun of 4.5 $\pm$ 0.6 kpc and that G10.3-0.1 may be associated with a
massive 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 two
components along the line of sight.
