This paper presents a new approach for mapping task graphs to heterogeneous hardware/software computing systems using heuristic search techniques. Two techniques: (1) integration of clustering, mapping, and scheduling in a single step and (2) multiple neighborhood functions strategy are proposed to enhance quality of mapping/scheduling solutions. Our approach is demonstrated by case studies involving 40 randomly generated task graphs, as well as four real applications including signal processing and pattern recognition. Experimental results show that the proposed integrated approach outperforms a separate approach in terms of quality of the mapping/scheduling solution by up to 18.3% for a heterogeneous system which includes a microprocessor, a floating-point digital signal processor, and an FPGA.