  We use high spectral resolution (R > 8000) data covering 3800-13000\r{A} to
study the physical conditions of the broad line region (BLR) of nine nearby
Seyfert 1 galaxies. Up to six broad HI lines are present in each spectrum. A
comparison - for the first time using simultaneous optical to near-infrared
observations - to photoionisation calculations with our devised simple scheme
yields the extinction to the BLR at the same time as determining the density
and photon flux, and hence distance from the nucleus, of the emitting gas. This
points to a typical density for the HI emitting gas of 10$^{11}$cm$^{-3}$ and
shows that a significant amount of this gas lies at regions near the dust
sublimation radius, consistent with theoretical predictions. We also confirm
that in many objects the line ratios are far from case B, the best-fit
intrinsic broad-line H$\alpha$/H$\beta$ ratios being in the range 2.5-6.6 as
derived with our photoionization modeling scheme. The extinction to the BLR,
based on independent estimates from HI and HeII lines, is A$_V$ $\le$ 3 for
Seyfert 1-1.5s, while Seyfert 1.8-1.9s have A$_V$ in the range 4-8. A
comparison of the extinction towards the BLR and narrow line region (NLR)
indicates that the structure obscuring the BLR exists on scales smaller than
the NLR. This could be the dusty torus, but dusty nuclear spirals or filaments
could also be responsible. The ratios between the X-ray absorbing column N$_H$
and the extinction to the BLR are consistent with the Galactic gas-to-dust
ratio if N$_H$ variations are considered.
