The Internet of Things (IoT) enables environmental monitoring by collecting data from sensing devices, including cameras and microphones. The popularity of smartphones enables mobile users to communicate and collect data from their surrounding sensing devices. The mobile devices can obtain useful environmental data from nearby sensors through short-range communication such as Bluetooth. Nevertheless, the limited contact time and the wireless capacity constrain the amount of data to be collected. With the increasing amount of multimedia big data such as videos and pictures from cameras, it is crucial for mobile users to collect prioritized data that can maximize their data utility. In this paper, we propose a distributed algorithm to provide information-centric ubiquitous data collection of multimedia big data by mobile users in the IoT. The algorithm can handle transmissions of multimedia big data recorded by the surrounding cameras and sensors, and prioritize the transmissions of the most important and relevant data. The mobile users construct data collection trees adaptively according to their dynamic moving speeds and the value of information carried by the multimedia and sensor data. The distributed algorithm can support smooth data collection and coordination of multiple mobile users. We provide both numerical analysis and extensive simulations to evaluate the information value, energy efficiency and scalability of our solution. The results showed that our distributed algorithm can improve the value of information up to 50% and reduce energy consumption to half compared with existing approach. Our algorithm also scales perfectly well with increasing number of mobile users and dynamic moving speeds.