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If you don't want to take a bus or the T, then you'll probably have to live either in Medford or Somerville. My suggestion is to take a look at padmapper.com and search for Tufts University--this will map out all the available apartments in the area. You might want to live to the south of campus, the "downhill" side, in Somerville. You'll be closer to Davis Square and its restaurants and bars, and to the T, which will make it easier to get into Cambridge and Boston. Teele Square, closer to campus than Davis, is another area to consider. It has a few restaurants and a bar, and from there it's a short walk to both campus and Davis Square.

Yes, that was 600 per person, so 1800 for the house. Public transportation in Medford/Somerville/Boston is pretty great, reliable buses and an excellent subway system, the T. You won't necessarily be living in Medford. Tufts is on the dividing line between Medford and Somerville, and Cambridge is also close by. From the redline T-stop in Davis Square, it's maybe a 10-15 minute walk to campus and a 2 minute bus trip. The area is also very bike-friendly. So, all in all, you can easily do without a car.

Hey, I went to Tufts for undergrad (English) and lived off-campus junior and senior years. I shared a house with two others and rent for 1 person was 600/month. This was a block or two from campus and I'm guessing there are cheaper places to be had. I'd be happy to answer any questions that come up. It's a great place to be! Congrats!