A coupled GaAs/AlGaAs quantum wire (QWR)-dot sample grown by molecular beam epitaxy on a patterned (311)A GaAs substrate is studied by near-field spectroscopy at a temperature of 10 K with a spectral resolution of 100 µeV. The two-dimensional potential energy profiles of the sample including localized excitonic states caused by structural disorder are determined in photoluminescence measurements with a spatial resolution of 150 nm. One finds a potential barrier of 20 meV between the quantum wire and the embedding quantum well (QW) on the mesa top of the structure. This is due to local thinning of the GaAs layer. In contrast, the wire-dot interface results free of energy barriers. The spatial variation of the GaAs layer thickness provides information on the growth mechanism determined by lateral diffusion of Ga atoms which is modeled by an analytical model. By performing spatially resolved photoluminescence excitation measurements on this wire-dot structure, we present a method for investigating carrier transport in low-dimensional systems: The dot area is used as an optical marker for excitonic diffusion via QW and QWR states. The two-dimensional (2D) and 1D diffusion coefficients are extracted as a function of the temperature and discussed.