This paper focuses on sequential and forward-looking behavior in destination choices of full-day. We can model the forward-looking behavior in the activity chain using a β-scaled recursive logit model that can not calculate future utility if the number of destination candidates is too large. Our primary objective is to construct a practical approach to sample destination alternatives. We propose a machine learning-based (ML) sampling approach by applying McFadden correction for choice set limitation to a β-scaled recursive logit model. Our supervised/unsupervised ML models are constructed using the activity history and enumerate among realistic alternatives considering the time-space prism constraint. We propose two sampling protocols: the supervised approach that samples using the decision tree rule constructed by observed choices by time and space; the unsupervised approach that samples from the constructed clusters using features of destinations. Our numerical test showed the estimability under the destination choice set by prism restriction and the proposed sampling. Our empirical case study using actual behavior data observed by smartphone-based GPS validated that our approaches improve the estimation stability of the time discount parameter. Our rule-based sampling protocol increased demand predictability compared to a simple random sampling protocol. The proposed method is practical because we can train the ML models using only observation data.