The Intensive Care Unit (ICU) serves as a critical resource in hospitals, delivering specialized care to patients with severe medical conditions. However, unplanned readmissions to the ICU pose significant challenges, including increased patient morbidity, extended hospital stays, and elevated healthcare costs. Predicting ICU readmissions is crucial for optimizing patient care and resource allocation. In this study, we explore the application of machine learning algorithms, including K-Neighbors Classifier, Random Forest Classifier, AdaBoost Classifier, Gradient Boosting Classifier, Logistic Regression, XGBoost Classifier, and Large Language Models (LLMs), to predict ICU readmissions. Leveraging data from the eICU Research Database, encompassing 166,355 patient admissions across 335 ICUs, our models were trained and evaluated using standard performance metrics. Results demonstrate that XGBoost achieved the highest overall performance, surpassing previous benchmarks. Notably, Gemma 2B LLM demonstrated strong predictive accuracy, highlighting its potential to improve outcomes in ICU settings. This study underscores the utility of advanced machine learning techniques and LLMs in improving healthcare outcomes by predicting ICU readmissions.