I am looking for an affordable 1-bedroom apartment close to Tufts University (even 25 minutes by train).?

Somerville will probably be the perfect place it is very close to tufts university. Somerville is also a lot cheaper than other parts of Boston. Other places to consider is Malden, Medford, or Melrose, but depending on the location, the train may not be close but buses definitely run through the area. Look on craigslist.com