TN, and in particular Chennai and Vellore, has been known to be a hub for advanced medical/tertiary healthcare and has been a host to a lot of Bengalis for decades now. Some of the medical institutions popular with Bengalis are the CMC, Apollo chain, Fortis Malar, Shankara Nethralaya, Global, etc. Of note, there is an area dedicated to Bengalis in Chennai, let me post an article in this regard for the reference of Bengalis here
click here which will surely help them during their stay here.