  We consider the discrete Gaussian Free Field (DGFF) in scaled-up
(square-lattice) versions of suitably regular continuum domains
$D\subset\mathbb C$ and describe the scaling limit, including local structure,
of the level sets at heights growing as a $\lambda$-multiple of the height of
the absolute maximum, for any $\lambda\in(0,1)$. We prove that, in the scaling
limit, the scaled spatial position of a typical point $x$ sampled from this
level set is distributed according to a Liouville Quantum Gravity (LQG) measure
in $D$ at parameter equal $\lambda$-times its critical value, the field value
at $x$ has an exponential intensity measure and the configuration near $x$
reduced by the value at $x$ has the law of a pinned DGFF reduced by a suitable
multiple of the potential kernel. In particular, the law of the total size of
the level set, properly-normalized, converges that that of the total mass of
the LQG measure. This sharpens considerably an earlier conclusion by Daviaud.
