The accurate calculation and uncertainty quantification of the characteristics of spent nuclear fuel (SNF) play a crucial role in ensuring the safety, efficiency, and sustainability of nuclear energy production, waste management, and nuclear safeguards. State of the art physics-based models, while reliable, are computationally intensive and time-consuming. This paper presents a surrogate modeling approach using neural networks (NN) to predict a number of SNF characteristics with reduced computational costs compared to physics-based models. An NN is trained using data generated from CASMO5 lattice calculations. The trained NN accurately predicts decay heat and nuclide concentrations of SNF, as a function of key input parameters, such as enrichment, burnup, cooling time between cycles, mean boron concentration and fuel temperature. The model is validated against physics-based decay heat simulations and measurements of different uranium oxide fuel assemblies from two different pressurized water reactors. In addition, the NN is used to perform sensitivity analysis and uncertainty quantification. The results are in very good alignment to CASMO5, while the computational costs (taking into account the costs of generating training samples) are reduced by a factor of 10 or more. Our findings demonstrate the feasibility of using NNs as surrogate models for fast characterization of SNF, providing a promising avenue for improving computational efficiency in assessing nuclear fuel behavior and associated risks.