Local electro-optic modulation of nanophotonic structures is important for many applications. Here, we show that one can achieve efficient tunability of the nanostructures by coupling them to graphene. The easy electrical control of graphene allows a large modulation of these graphene-clad nanophotonic devices. We describe electrostatic tuning of a metallic as well as a dielectric resonator coupled to graphene. A large change, both in resonator linewidth and resonance frequency is observed. The experimental data match the theory very well indicating that the changes in the resonator are solely coming due to graphene.