In classical general relativity, the mass of a Schwarschild black hole is associated with its singularity. The simplest argument for this, is that the Schwarzschild metric (and its full analytic extension) is a solution to the vacuum Einstein equations. Hence there is no mass, anywhere in the manifold, "hence" the mass must be associated with the only part that is not on the manifold, the singularity.
However, this is not a very satisfying argument. It does not take into account the many subtleties surrounding the definition of mass in general relativity. It is therefore worth looking at a more rigorous argument. The right tool for the job is the Komar mass. (The ADM mass is only defined at spatial infinity, and therefore does not allow us to ask where the mass is located)
The Komar mass can be defined for any stationary spacetime.
The Komar surface integral is given by
$$ M = \frac{c^2}{4\pi G}\oint_S \nabla^\mu K^\nu dS_{\mu\nu} ,$$
where $S$ is a 2-dimensional closed spacelike surface, $S_{\mu\nu}$ is the surface element of $S$, and $K^\mu$ is a time-like Killing vector field normalized such that $K^\mu K^\mu = -1$ at spatial infinity. It measures the mass contained within the boundary $S$.
If we look at the ingoing Eddington-Finkelstein extension, and calculate the Komar surface integral for a surface with fixed radius $r$ and advanced time $v$ (left as an exercise for the curious reader), we find that is always equals $M$ the total mass of the Schwarzschild black hole. This tells us that the mass of this manifold is located around the singularity at $r=0$, and in particular shows that there is no mass associated with region around the horizon.
Of course, this is the answer according to classical general relativity. In a theory of quantum gravity the answer might end up being substantially different. For example, in the string theory inspired fuzzball picture, the mass would be associated with a quantum state that has the approximate size of the horizon.
