In this work we study the behavior of classical two-person, two-strategies evolutionary games on networks embedded in a Euclidean two-dimensional space with different kinds of degree distributions and topologies going from regular to random, and to scale-free ones. Using several imitative microscopic dynamics, we study the evolution of global cooperation on the above network classes and find that specific topologies having a hierarchical structure and an inhomogeneous degree distribution, such as Apollonian and grid-based networks, are very conducive to cooperation. Spatial scale-free networks are still good for cooperation but to a lesser degree. Both classes of networks enhance average cooperation in all games with respect to standard random geometric graphs and regular grids by shifting the boundaries between cooperative and defective regions. These findings might be useful in the design of interaction structures that maintain cooperation when the agents are constrained to live in physical two-dimensional space.