The surging traffic volumes and dynamic user mobility patterns pose great challenges for cellular network operators to reduce operational costs and ensure service quality. Cloud-radio access network (C-RAN) aims to address these issues by handling traffic and mobility in a centralized manner, separating baseband units (BBUs) from base stations (RRHs) and sharing BBUs in a pool. The key problem in C-RAN optimization is to dynamically allocate BBUs and map them to RRHs under cost and quality constraints, since real-world traffic and mobility are difficult to predict, and there are enormous numbers of candidate RRH-BBU mapping schemes. In this work, we propose a data-driven framework for C-RAN optimization. First, we propose a deep-learning-based Multivariate long short term memory (MuLSTM) model to capture the spatiotemporal patterns of traffic and mobility for accurate prediction. Second, we formulate RRH-BBU mapping with cost and quality objectives as a set partitioning problem, and propose a resource-constrained label-propagation (RCLP) algorithm to solve it. We show that the greedy RCLP algorithm is monotone suboptimal with worst-case approximation guarantee to optimal. Evaluations with real-world datasets from Ivory Coast and Senegal show that our framework achieves a BBU utilization above 85.2 percent, with over 82.3 percent of mobility events handled with high quality, outperforming the traditional and the state-of-the-art baselines.