Migrating cells often encounter a wide variety of topographic features— including the presence of obstacles— when navigating through crowded biological environments. Unravelling the impact of topography and crowding on the dynamics of cells is key to better understand many essential physiological processes such as the immune response. We study the impact of geometrical cues on amoeboid migration of HL-60 cells differentiated into neutrophils. A microfluidic device is designed to track the cells in confining geometries between two parallel plates with distance h, in which identical micropillars are arranged in regular pillar forests with pillar spacing e. We observe that the cells are temporarily captured near pillars, with a mean contact time which is independent of h and e. By decreasing the vertical confinement h, we find that the cell velocity is not affected while the persistence reduces; thus, cells are able to preserve their velocity when highly squeezed but lose the ability to control their direction of motion. At a given h, we show that by decreasing the pillar spacing e in the weak lateral confinement regime, the mean escape time of cells from effective local traps between neighboring pillars grows. This effect, together with the increase of cell-pillar contact frequency, leads to the reduction of diffusion constant D. By disentangling the contributions of these two effects on D in numerical simulations, we verify that the impact of cell-pillar contacts on cell diffusivity is more pronounced at smaller pillar spacing.