This problem describes a recommendation system with millions of records, many categorical variables, and a high-dimensional sparse feature space created by one-hot encoding. AWS documentation explicitly recommends Amazon SageMaker Factorization Machines (FM) for such use cases.

Factorization Machines are designed to handle sparse datasets efficiently and to model interactions between categorical features without explicitly enumerating all feature combinations. This capability makes FM particularly well-suited for recommendation problems such as predicting user-item interactions, including destination recommendations.

With 2,000 possible airport destinations, the target space is large and sparse. One-hot encoding further increases sparsity. Factorization Machines address this challenge by learning latent factors that capture relationships between features, even when many feature combinations are rarely observed.

Option A (CatBoost) is not an Amazon SageMaker built-in algorithm and therefore does not meet the requirement. Option B (DeepAR) is a time-series forecasting algorithm, not intended for recommendation or classification problems. Option D (k-means) is an unsupervised clustering algorithm and cannot directly predict a specific destination label.

AWS documentation explicitly lists recommendation systems and click prediction as primary use cases for the SageMaker Factorization Machines algorithm.

Therefore, Option C is the correct and AWS-verified choice.