  We consider four-dimensional $N=2$ supergravity coupled to vector- and
hypermultiplets, where abelian isometries of the quaternionic K\"ahler
hypermultiplet scalar manifold are gauged. Using the recipe given by Meessen
and Ort\'{\i}n in arXiv:1204.0493, we analytically construct a supersymmetric
black hole solution for the case of just one vector multiplet with prepotential
${\cal F}=-i\chi^0\chi^1$, and the universal hypermultiplet. This solution has
a running dilaton, and it interpolates between $\text{AdS}_2\times\text{H}^2$
at the horizon and a hyperscaling-violating type geometry at infinity,
conformal to $\text{AdS}_2\times\text{H}^2$. It carries two magnetic charges
that are completely fixed in terms of the parameters that appear in the Killing
vector used for the gauging. In the second part of the paper, we extend the
work of Bellucci et al. on black hole attractors in gauged supergravity to the
case where also hypermultiplets are present. The attractors are shown to be
governed by an effective potential $V_{\text{eff}}$, which is extremized on the
horizon by all the scalar fields of the theory. Moreover, the entropy is given
by the critical value of $V_{\text{eff}}$. In the limit of vanishing scalar
potential, $V_{\text{eff}}$ reduces (up to a prefactor) to the usual black hole
potential.
