Many processes within galaxy clusters, such as those believed to govern the onset of thermally unstable cooling and AGN feedback, are dependent upon local dynamical timescales. However, accurately mapping the mass distribution within individual clusters is challenging, particularly towards cluster centres where the total mass budget has substantial radially-dependent contributions from the stellar, gas, and dark matter components. In this paper we use a small sample of galaxy clusters with deep Chandra observations and good ancillary tracers of their gravitating mass at both large and small radii to develop a method for determining mass profiles that span a wide radial range and extend down into the central galaxy. We also consider potential observational pitfalls in understanding cooling in hot cluster atmospheres, and find tentative evidence for a relationship between the radial extent of cooling X-ray gas and nebular H-alpha emission in cool core clusters. Amongst this small sample we find no support for the existence of a central 'entropy floor', with the entropy profiles following a power-law profile down to our resolution limit. ; Comment: 15 pages, 9 figures, 2 tables. Submitted to ApJ