Predicting human mobility within cities is an important task in urban and transportation planning. With the vast amount of digital traces available through social media platforms, we investigate the potential application of such data in predicting commuter trip distribution at small spatial scale. We develop back propagation (BP) neural network and gravity models using both traditional and Twitter data in New York City to explore their performance and compare the results. Our results suggest the potential of using social media data in transportation modeling to improve the prediction accuracy. Adding Twitter data to both models improved the performance with a slight decrease in root mean square error (RMSE) and an increase in R-squared (R2) value. The findings indicate that the traditional gravity models outperform neural networks in terms of having lower RMSE. However, the R2 results show higher values for neural networks suggesting a better fit between the real and predicted outputs. Given the complex nature of transportation networks and different reasons for limited performance of neural networks with the data, we conclude that more research is needed to explore the performance of such models with additional inputs.