Destination choice models are a crucial subset of the activity-based approach to travel modeling. In this approach, modeling is performed continuously, using the results of previous models in subsequent ones. For estimating destination choice models, it is necessary first to estimate the mode choice model and then incorporate its effect on individuals' destination choices. Moreover, a significant challenge in estimating destination choice models is the large number of available options (zones). When estimating these models using discrete choice models, typically formulated as logit models, the computational time increases significantly, or it may even become infeasible. Therefore, it is necessary first to select a city from among all cities as a choice set, and then predict the target zone within the chosen city. This hierarchical selection method is referred to as a choice set. For this purpose, a neural network model was implemented to analyze the data and predict the destination choice. The accuracy of these models was 73% for the city level and 23% for the zone level. This indicates that the neural network model demonstrated a considerable improvement in predictive power compared to the multinomial logit model in destination choice modeling. These models were applied to data from Washington, D.C., and the results suggest that estimating destination choice using a neural network has shown improved predictive performance in discrete choice modeling.