Brighton Center might work. There is an express bus with somewhat limited hours that gets downtown fast. (What do you mean by "downtown"?) Other, regular, buses like the 57, 65, and 86 can get you to the T (either Green Line or Red Line at Harvard).
Since you have a car another possibility is the area in Belmont and Watertown along the 73 bus. My girlfriend lives here, on the Belmont side a few blocks from the Cambridge line, and takes the bus 15 min. to Harvard Sq. and then it's a quick trip downtown on the Red Line. She's got a great place there and there are nice and big apartments for less than at Harvard or Davis, or anywhere in Cambridge really. It's a little quieter than Brighton but not as quiet as Braintree or Arlington. The best search on boston.craigslist.org would be "Belmont Harvard" or "Watertown Harvard" The closer to Harvard the better since the bus takes longer the farther out you are.
$1500 for 2-BR in a safe area with quick access by T to downtown is not always easy but these areas strike a pretty good balance.
Here's a couple of ads not far from my girlfriend's:
2nd Floor Apartment (broken link)
half fee DELEADED Garage Av 3/1 Harvard Lawn