We study the evolution of cooperation in the prisoner's dilemma game on time-invariant heterogeneous payoff landscapes on regular and heterogeneous networks. Correlations in the landscape structure and their implications for the evolution of cooperation are investigated. On regular networks we find that negatively and neutrally correlated payoff landscapes strongly enhance cooperation, while positively correlated landscapes may suppress the evolution of cooperation. On heterogeneous networks, cooperation is facilitated if payoff stochasticity is positively correlated with network heterogeneity and may be suppressed otherwise.