Synchronization is fundamental for information processing in oscillatory brain networks and is strongly affected by time delays via signal propagation along long fibers. Their effect, however, is less evident in spiking neural networks given the discrete nature of spikes. To bridge the gap between these different modeling approaches, we study the synchronization conditions, dynamics underlying synchronization, and the role of the delay of a two-dimensional network model composed of adaptive exponential integrate-and-fire neurons. Through parameter exploration of neuronal and network properties, we map the synchronization behavior as a function of unidirectional long-range connection and the microscopic network properties and demonstrate that the principal network behaviors comprise standing or traveling waves of activity and depend on noise strength, E/I balance, and voltage adaptation, which are modulated by the delay of the long-range connection. Our results show the interplay of micro- (single neuron properties), meso- (connectivity and composition of the neuronal network), and macroscopic (long-range connectivity) parameters for the emergent spatiotemporal activity of the brain.