Tina Evans, Principal Broker
Two areas come to mind, Natick and West Roxbury. Both areas have homes in your price range, offer a location closer to Boston, and have some form of public transportation. Unfortnately, most of the other towns east of Framingham do not offer much choice under $400K for a single family home.
Feel free to browse MLS which is available on my website or call me with any specific questions you may have.
Your budget can actually take you pretty far it just depends on how much space you need ... i.e, what is your bedroom criteria, etc. The closer you get to Boston the more valuable the house ... This is true in any metropolitan city so I think it is definitely worth considering. The downside is usually the closer you get to boston the less space you get for the money, but if your are diligent in your search you will likely find the perfect balance.
Here are a few examples for needham, arlington, waltham and watertown (all east, some a little north and south):
Hope that helps give you an idea. If you post your criteria we might be able to help you better. Good luck!