Micro- and nano-optomechanical systems have been widely investigated for displacement and force sensing and find application in atomic-force microscopy (AFM) and fiber-tip sensing. The usual AFM read-out method, based on position-sensitive detection of the cantilever reflection, combines high resolution and dynamic range, but it cannot be easily integrated. Recently, nanophotonic cavities have shown the potential for high-resolution displacement sensing on an integrated chip. However, the resonant nature of the cavity response intrinsically limits the dynamic range and the optical bandwidth, putting stringent requirements on the read-out system. Here we present an integrated sensor which employs an on-chip nanomechanical directional coupler rather than a cavity for the transduction, and combines a displacement imprecision <50 fm Hz-1/2 with a relatively large displacement dynamic range and broad optical linewidth. An integrated Indium Phosphide (InP) photodiode is used for the readout, greatly reducing packaging complexity.