Long oligomer sequences, rich in guanine and cytosine, such as c-kit1 and the HIV-1 LTR-III sequence, are prevalent in oncogenes and retroviruses and play crucial roles in cancer. Understanding the conformational dynamics of such guanine quadruplexes and identifying druggable regions are therefore essential for developing new inhibition strategies. In this study, we used extensive AMOEBA polarizable force field molecular dynamics simulations combined with data-driven adaptive sampling and clustering algorithms, reaching a cumulative simulation time of 7.5 $\mu$s for c-kit1. Our results reveal novel structural stabilizations and flexible loop dynamics, as well as the critical role of polarizable water in stabilizing the G-quadruplex, leading to the identification of two new druggable pockets in c-kit1. Additionally, 400 ns simulation of the HIV-1 LTR-III sequence confirmed its quadruplex stability and uncovered a potentially druggable cryptic pocket.