This paper goes beyond classic Internet of Things (IoT) and focuses on the concept of Multimedia-based Internet of Things (M-IoT). Smart heterogeneous multimedia things can interact and cooperate with each another and with other things connected to the Internet to facilitate multimedia-based services and applications that are globally available to the users. Nowadays, the access network selection for heterogeneous multimedia devices is not managed taking into account the reputation that a given network has at a given instant. In order to solve these issues ReMIoT, a Reputation-based M-IoT architecture is introduced in this paper and presented alongside a novel solution to improve multimedia content delivery quality. The solution includes three distinct operational stages: (i) multimedia service detection, (ii) network reputation detection, and (iii) M-IoT network selection. The performance of the proposed solution is compared against that of a traffic type-based differentiated reputation algorithm for radio resource allocation (TYDER). This performance was evaluated in terms of QoS parameters such as throughput, packet delay and packet loss ratio.