my old place was a bus ride to campus. this is not my real address but within the vicinity:http://maps.google.com/maps?q=300+broad ... CAgQ8gEwAA
i don't think you could get a studio within walking distance to HLS for that price. you could probably get a studio in the porter/davis area for ~ $1100 though, which is worth the upgrade over my old place in my opinion. a 1BR in porter/davis would be roughly $1300.
trying to get a place in/near harvard square probably adds 100-200 dollars to the rent. if you are willing to live in the less prestigious somerville, you can usually save 100-200 off the prices i listed
. davis/porter are on the somerville/cambridge line so there are plenty of convenient places in somerville as well.