We consider the k-Center problem and some generalizations. For k-Center a set of k center vertices needs to be found in a graph G with edge lengths, such that the distance from any vertex of G to its nearest center is minimized. This problem naturally occurs in transportation networks, and therefore we model the inputs as graphs with bounded highway dimension, as proposed by Abraham et al. [ICALP 2011]. We show both approximation and fixed-parameter hardness results, and how to overcome them using fixed-parameter approximations. In particular , we prove that for any ε > 0 computing a (2 − ε)-approximation is W[2]-hard for parameter k, and NP-hard for graphs with highway dimension O(log 2 n). The latter does not rule out fixed-parameter (2 − ε)-approximations for the highway dimension parameter h, but implies that such an algorithm must have at least doubly exponential running time in h if it exists, unless the ETH fails. On the positive side, we show how to get below the approximation factor of 2 by combining the parameters k and h: we develop a fixed-parameter 3/2-approximation with running time 2 O(kh log h) · n O(1). We also provide similar fixed-parameter approximations for the weighted k-Center and (k, F)-Partition problems, which generalize k-Center.