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Neural methods are state-of-the-art for urban prediction problems such as transportation resource demand, accident risk, crowd mobility, and public safety. Model performance can be improved by integrating exogenous features from open data repositories (e.g., weather, housing prices, traffic, etc.), but these uncurated sources are often too noisy, incomplete, and biased to use directly. We propose to learn integrated representations, called EquiTensors, from heterogeneous datasets that can be reused across a variety of tasks. We align datasets to a consistent spatio-temporal domain, then describe an unsupervised model based on convolutional denoising autoencoders to learn shared representations. We extend this core integrative model with adaptive weighting to prevent certain datasets from dominating the signal. To combat discriminatory bias, we use adversarial learning to remove correlations with a sensitive attribute (e.g., race or income). Experiments with 23 input datasets and 4 real applications show that EquiTensors could help mitigate the effects of the sensitive information embodied in the biased data. Meanwhile, applications using EquiTensors outperform models that ignore exogenous features and are competitive with "oracle" models that use hand-selected datasets.