Boston hotels are indeed expensive but I can surely guarantee that staying in the Financial District will be a good return on investment for you. Boston has good and bad parts and hardly anything in between. Cambridge (Harvard and MIT area) is pleasant but it's mainly a college town so clientele will be almost non-existent.
I had a friend who while she was there, a guy posed as a cop and did a damn good job. Other than that imposter, I've heard LE is pretty stringent there so be careful.
Other than that, make sure you try their cannolis!