Granulomas are complex lung lesions that are the hallmark of tuberculosis (TB). Understanding antibiotic dynamics within lung granulomas will be vital to improving and shortening the long course of TB treatment. Three fluoroquinolones (FQs) are commonly prescribed as part of multi-drug resistant TB therapy: moxifloxacin (MXF), levofloxacin (LVX) or gatifloxacin (GFX). To date, insufficient data are available to support selection of one FQ over another, or to show that these drugs are clinically equivalent. To predict the efficacy of MXF, LVX and GFX at a single granuloma level, we integrate computational modeling with experimental datasets into a single mechanistic framework, GranSim. GranSim is a hybrid agent-based computational model that simulates granuloma formation and function, FQ plasma and tissue pharmacokinetics and pharmacodynamics and is based on extensive in vitro and in vivo data. We treat in silico granulomas with recommended daily doses of each FQ and compare efficacy by multiple metrics: bacterial load, sterilization rates, early bactericidal activity and efficacy under non-compliance and treatment interruption. GranSim reproduces in vivo plasma pharmacokinetics, spatial and temporal tissue pharmacokinetics and in vitro pharmacodynamics of these FQs. We predict that MXF kills intracellular bacteria more quickly than LVX and GFX due in part to a higher cellular accumulation ratio. We also show that all three FQs struggle to sterilize non-replicating bacteria residing in caseum. This is due to modest drug concentrations inside caseum and high inhibitory concentrations for this bacterial subpopulation. MXF and LVX have higher granuloma sterilization rates compared to GFX, and MXF performs better in a simulated non-compliance or treatment interruption scenario. We conclude that MXF has a small but potentially clinically significant advantage over LVX, as well as LVX over GFX. We illustrate how a systems pharmacology approach combining experimental and computational methods can guide antibiotic selection for TB.