I grew up in that area (Weston/Wellesley/Natick). Its a nice area with good access to boston and western mass via Mass Pike and Route 9. Although, I cannot speak for the residents I know that many people in that area live at the Edgewater Apartments located directly on Route 9. There are about a dozen or so different buildings there with different layouts, prices, etc. You could probably hit them all up in a day or so and get information, etc. I am sure there are smaller apartment buildings or complexes closer to the hospital itself but this is just an idea. Good luck.
care
