Collecting user's current location(s) and place-to-place transitions, predicting future destinations, equipping users with location sensitive information, and handling relevant communication requests are core ingredients of new generation of service provider applications on mobile devices. Periodic place-to-place transitions are inherent in human movements. Next place predictions are the atomic units in constructing end-to-end user mobility trajectories based on historical trace data. We make next place predictions by recognizing and utilizing periodicity in user mobility traces. We start with a baseline of the user's current place, start time, and end time to predict the next place. We demonstrate the efficiency of our algorithms through aggregated average prediction accuracies across all users over a large set of diverse participants. We improve these predictions through existing semantic information in the trace data sets, deduced place semantics, and other temporal considerations from the trace data.