Heavy quarkonia production is predicted to be sensitive to the formation of the quark gluon plasma in relativistic heavy ion collisions via competing mechanisms such as color screening and/or quark recombination. The PHENIX collaboration has measured $J/\psi$ decay into lepton pairs in Au+Au and Cu+Cu collisions at $\sqrt{s_{NN}}=200$~GeV. The nuclear modification factor $R_{AA}$ for the $J/\psi$ is obtained by comparing Au+Au or Cu+Cu collisions to p+p collisions. The $R_{AA}$ dependence over centrality, transverse momentum and rapidity will be presented both at forward rapidity ($1.2<|\eta|<2.2$) using $J/\psi\rightarrow\mu^+\mu^-$ and at mid rapidity ($|\eta|<0.35$) using $J/\psi\rightarrow e^+e^-$. It will be compared to theoretical predictions and to results obtained from collisions with lighter nuclei.