We consider the distribution of waiting times between noninteracting fermions on a tight-binding chain. We calculate the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off as predicted by scattering theory. In addition, we consider several quantum dot structures for which we can associate oscillations in the waiting time distributions with internal energy scales of the scatterers. A detailed comparison with scattering theory and generalized master equations is provided. We focus on mesoscopic conductors, but our tight-binding models may also be realized in cold-atomic gases.