Single-point measurements from towers in cities cannot properly quantify the impact of all terms in the turbulent kinetic energy (TKE) budget and are often not representative of horizontally-averaged quantities over the entire urban domain. A series of large-eddy simulations (LES) is here performed to quantify the relevance of non-measurable terms, and to explore the spatial variability of the flow field over and within an urban geometry in the city of Basel, Switzerland. The domain has been chosen to be centered around a tower where single-point turbulence measurements at six heights are available. Buildings are represented through a discrete-forcing immersed boundary method and are based on detailed real geometries from a surveying dataset. The local model results at the tower location compare well against measurements under near-neutral stability conditions and for the two prevailing wind directions chosen for the analysis. This confirms that LES in conjunction with the immersed boundary condition is a valuable model to study turbulence and dispersion within a real urban roughness sublayer (RSL). The simulations confirm that mean velocity profiles in the RSL are characterized by an inflection point zγ located above the average building height zh. TKE in the RSL is primarily produced above zγ, and turbulence is transported down into the urban canopy layer. Pressure transport is found to be significant in the very-near-wall regions. Further, spatial variations of time-averaged variables and non-measurable dispersive terms are important in the RSL above a real urban surface and should therefore be considered in future urban canopy parametrization developments.