Using molecular dynamics experiments, we have extended our previous analysis of equimolar mixtures of water and acetonitrile confined between silica walls [J. Phys. Chem. B 2009, 113, 12744] to examine similar solutions trapped within carbon nanotubes and cylindrical silica pores. Two different carbon tube sizes were investigated, (8,8) tubes, with radius R_cnt = 0.55 nm, and (16,16) ones, with R_cnt = 1.1 nm. In the narrowest tubes, we found that the cylindrical cavity is filled exclusively by acetonitrile; as the radius of the tube reaches ~1 nm, water begins to get incorporated within the inner cavities. In (16,16) tubes, the analysis of global and local concentration fluctuations shows a net increment of the global acetonitrile concentration; in addition, the aprotic solvent is also the prevailing species at the vicinity of the tube walls. Mixtures confined within silica nanopores of radius ~1.5 nm were also investigated. Three pores, differing in the effective wall/solvent interactions, were analyzed, (i) a first class, in which dispersive forces prevail (hydrophobic cavities), (ii) a second type, where oxygen sites at the pore walls are transformed into polar silanol groups (hydrophilic cavities), and (iii) finally, an intermediate scenario, in which 60% of the OH groups are replaced by mobile trimethylsilyl groups. Within the different pores, we found clear distinctions between the solvent layers that lie in close contact with the silica substrate and those with more central locations. Dynamical modes of the confined liquid phases were investigated in terms of diffusive and rotational time correlation functions. Compared to bulk results, the characteristic time scales describing different solvent motions exhibit significant increments. In carbon nanotubes, the most prominent modifications operate in the narrower tubes, where translations and rotations become severely hindered. In silica nanopores, the manifestations of the overall retardations are more dramatic for solvent species lying at the vicinity of trimethylsilyl groups.