Applications of liquid crystals (LCs) are based on controlling the orientational and translational order of the medium. One important way of control is via confinement. In this work, uniaxial thermotropic LCs confined to nanosized cylindrical cavities are studied using isobaric parallel tempering (PT) Monte Carlo (MC) simulations. The LCs are modeled using the Gay-Berne (4.4, 20.0, 1, 1) (GB) potential in long, smooth-walled cavities. The chosen particle-wall interaction favours homogeneous planar anchoring the alignment of molecules along the wall. We report the results for the phase structure appropriate to three different cavity sizes as well as comparison to the results of bulk simulations. Ensemble averages for orientational and translational order parameters as well as their local behavior as a function of the distance to the cavity wall is calculated by reweighting results from all the simulated temperatures. We find that the LC director tends to align strongly with the axis of the cylindrical cavity. The orientational order is enhanced and translational order suppressed by the walls of the cavity. Hence, there are notable differences between the local order close to the wall and near the cylinder axis. The position-dependent distributions of the order parameters result in smooth phase transitions in their respective system-wide averages. Particularly, the nematic-isotropic (N-I) transition is replaced by a continuous nematic-paranematic (N-PN) transition. This is caused by the core region of the cavities becoming isotropic at high temperatures, whereas near the wall the LC retains nematic order. In contrast to previous NVT ensemble simulations, we find the effect of confinement on the smectic (Sm) layering to be weak. Also, Sm-N and N-PN transitions are found to be both sharper and residing at higher temperatures than in the constant-volume simulations. At temperatures where the bulk LC is a solid, we observe a wall-induced density wave in the confined systems, which outweighs the self-organization of the LC to hexagonal in-plane order.