  A $k$-coloring of a graph $G$ is a partition of the set of vertices of $G$
into $k$ independent sets, which are called colors. A $k$-coloring is
neighbor-locating if any two vertices belonging to the same color can be
distinguished from each other by the colors of their respective neighbors. The
neighbor-locating chromatic number $\chi _{_{NL}}(G)$ is the minimum
cardinality of a neighbor-locating coloring of $G$. In this paper, we determine
the neighbor-locating chromatic number of paths, cycles, fans, and wheels.
Moreover, a procedure to construct a neighbor-locating coloring of minimum
cardinality for these families of graphs is given. We also obtain tight upper
bounds on the order of trees and unicyclic graphs in terms of the
neighbor-locating chromatic number. Further partial results for trees are also
established.
