Active control of spin-wave dynamics is demonstrated using broadband ferromagnetic resonance in two-dimensional Ni80Fe20 antidot lattices arranged in hexagonal lattice with fixed lattice constant but varying antidot diameter. A strong modification in the spin-wave spectra is obtained with the variation in the antidot diameter as well as with the strength and orientation of the bias magnetic field. A broad band of modes is observed for the lattice with higher antidot diameter which decreases systematically as the antidot diameter is reduced. A crossover between the higher frequency branches is achieved in lattices with higher antidot diameter. In addition, the spin-wave modes in all lattices show a strong six-fold anisotropic behaviour due to the variation of internal field distribution as a function of the bias-field orientation. A mode hopping-like behavior is observed in the angular dispersions of spin-wave spectra for samples having intermediate hole diameters. Micromagnetic simulations qualitatively reproduce the experimentally observed spin-wave modes and the simulated mode profiles reveal the presence of extended and quantized standing spin-wave modes in these lattices. These observations are significant for large tunability and anisotropic propagation of spin waves in GHz frequency magnetic devices.