The spontaneous emission and energy transfer rates of quantum systems in proximity to a dielectrically coated metallic cylinder are investigated using a Green's tensor formalism. The excitation of surface plasmon modes can significantly modify these rates. The spontaneous emission and energy transfer rates are investigated as a function of the material and dimensions of the core and coating, as well as the emission wavelength of the donor. For the material of the core we consider gold and silver, whose surface plasmon wavelengths lie in the visible part of the electromagnetic spectrum. The spontaneous emission rate is enhanced by several orders of magnitude when the emission wavelength is close to the surface plasmon wavelength. The energy transfer rate enhancement is found to be concentrated in hot spots around the circumference of the coated cylinder. Introducing the energy transfer efficiency as a parameter, we find that, when the donor emission and acceptor absorption spectra are resonant with the surface plasmon modes excited on the coated cylinder, the energy transfer efficiency can be significantly enhanced compared to the off-resonance situation. Tuning the surface plasmon wavelength to the emission wavelength of the donor via the geometrical and material parameters of the coated cylinder allows, therefore, control of the energy transfer efficiency.