This paper presents a comprehensive analysis of sentiment and topic trends in tweets related to several US universities. By employing sentiment analysis techniques, such as VADER and BERT-based, and topic modeling methods, such as Non-negative Matrix Factorization (NMF), we explore the dynamics of Twitter discourse around significant peaks and dips in sentiment values. We analyze datasets for days with extreme sentiment scores and high tweet counts, focusing on universities like Princeton, Stanford, and UC Berkeley, and perform detailed analyses of individual tweets to provide granular insights into specific events and narratives driving sentiment shifts. This detailed examination helps to contextualize broader trends and offers a nuanced understanding of the factors influencing public perception and engagement with universities on social media. Our findings underscore the variability in university-related Twitter discourse and demonstrate the efficacy of traditional and advanced NLP techniques for comprehensive sentiment and topic analysis. This study contributes to understanding social media dynamics in educational contexts and provides a methodological framework for similar analyses.