Understanding mobility characteristics is important for the design and analysis of routing schemes for mobile ad hoc networks (MANETs). This is especially true for mobile opportunistic networks where node mobility is utilized to achieve message delivery. In this paper, we study the properties of common mobility models. Specifically, we study inter-contact times of mobile nodes in Random Waypoint and Random Direction mobility models under opportunistic network settings. We also introduce a modified Random Waypoint model with hot-spots to study its mobility properties. Through extensive simulation study, we provide simulation results for mobility properties of Random Waypoint and Random Direction models. Further, our modified Random Waypoint with hot-spots model is also found to show an approximate power-law and exponential inter-contact time dichotomy found in real-world mobility traces as described in recent literature.