We consider degree-biased random walkers whose probability to move from a node to one of its neighbors of degree \(k\) is proportional to \(k^{\alpha}\), where \(\alpha\) is a tuning parameter. We study both numerically and analytically three types of characteristic times, namely: i) the time the walker needs to come back to the starting node, ii) the time it takes to visit a given node for the first time, and iii) the time it takes to visit all the nodes of the network. We consider a large data set of real-world networks and we show that the value of \(\alpha\) which minimizes the three characteristic times is different from the value \(\alpha_{\rm min}=-1\) analytically found for uncorrelated networks in the mean-field approximation. In addition to this, we found that assortative networks have preferentially a value of \(\alpha_{\rm min}\) in the range \([-1,-0.5]\), while disassortative networks have \(\alpha_{\rm min}\) in the range \([-0.5, 0]\). We derive an analytical relation between the degree correlation exponent \(\nu\) and the optimal bias value \(\alpha_{\rm min}\), which works well for real-world assortative networks. When only local information is available, degree-biased random walks can guarantee smaller characteristic times than the classical unbiased random walks, by means of an appropriate tuning of the motion bias.