Description of the local microscopic structure in ionic liquids (ILs) is a prerequisite to obtain a comprehensive understanding of the influence of the nature of ions on the properties of ILs. The local structure is mainly determined by the spatial arrangement of the nearest neighboring ions. Therefore, the main interaction patterns in ILs, such as cation-anion H-bond-like motifs, cation-cation alkyl tail aggregation, and ring stacking, were considered within the framework of the nearest-neighbor approach with respect to each particular interaction site. We employed classical molecular dynamics (MD) simulations to study in detail the spatial, radial, and orientational relative distribution of ions in a set of imidazolium-based ILs, in which the 1-butyl-3-methylimidazolium (C(4)mim(+)) cation is coupled with the acetate (OAC(-)), chloride (Cl-, tetrafluoroborate (BF4-, hexafluorophosphate (PF6-), trifluoromethanesulfonate (TfO-, or bis(trifluoromethanesulfonyl)amide (TFSA(-)) anion. It was established that several structural properties are strongly anion-specific, while some can be treated as universally applicable to ILs, regardless of the nature of the anion. Namely, strongly basic anions, such as OAC(-) and Cl-, prefer to be located in the imidazolium ring plane next to the C-H2/4-5 sites. By contrast, the other four bulky and weakly coordinating anions tend to occupy positions above/below the plane. Similarly, the H-bond-like interactions involving the H-2 site are found to be particularly enhanced in comparison with the ones at H4-5 in the case of asymmetric and/or more basic anions (C(4)mimOAc, C(4)mimCl, C(4)mimTfO, and C(4)mimTFSA), in accordance with recent spectroscopic and theoretical findings. Other IL-specific details related to the multiple H-bond-like binding and cation stacking issues are also discussed in this paper. The secondary H-bonding of anions with the alkyl hydrogen atoms of cations as well as the cation-cation alkyl chain aggregation turned out to be poorly sensitive to the nature of the anion.