The radius and lattice constant are as fundamental to your operation of a photonic crystal as the material it is made out of. The r/a ratio will control the size and location of your band gap versus wa/2pic, see the gap maps in Appendix C of the first edition of Photonic Crystals: Molding the Flow of Light.
As your operating wavelength is typically chosen to be in the center of the bandgap you look at a gap map and determine the widest gap and note that r/a and convert the wa/2pic range to as close to your desired frequency range by choosing a then from the previously noted r/a you get your required radius.