Right neighborhood for international student at Texas Medical Center, prefer not to have to drive

I am an Indian in my mid 20s who is moving to Houston to study at UTHealth, December 2020 onwards. I am looking for a place (there will be two of us) near SBMI, UTHealth and I do not want to drive as part of my commute. Can you please suggest good neighborhoods where I can find gated communities with good amenities and easy access to public transport? As two young men in our twenties, we would prefer places near good nightlife and fun things to do. P.S. Is bus/train transport reliable enough to use at all times of the day? Our budget would be anything under $1400 for a two bedroom 2 bathroom place. Thanks. 🙂