Hey Dave9,
Also an incoming intern -- I'm starting categorical medicine.
I spent a good bit of time driving around on the east side, looking at places listed on craigslist, at least from the outside. I agree with what others have said that for $1400 you'll have no problem finding a very comfortable place. I can't remember if you're looking for a 1 or 2 BR, but even for a 2 BR that's within the range for the east side. I think that once you come back in June you'll be able to find a place to rent. I found driving around the city very helpful in terms of figuring out where I imagined I'd have everything I wanted (and therefore likely *not* to want to move because I'm tired of moving!)
I would add to your considerations whether you want to live around many undergraduates or not. I found some of the areas in fox point to be a little heavily populated by undergrads/early grad students -- apartments seemed slightly more run down, and in one apartment I visisted, the neighbors upstairs were blaring loud music with the windows open. I decided I was looking for more quiet environs -- a clear sign that I'm getting old!
I don't know if you've looked at the Brown off-campus listings, but that's where I found my apartment. I also saw a 1 BR on Moses Brown St listed that seemed really promising -- right in wayland square, and equidistant (basically) to RIH and Miriam. I didn't end up looking at it because I ended up signing a lease for another apartment before I saw the Moses Brown one.
So I concur that providence.craigslist.org and the brown off-campus listings are your best bet.
Also, I definitely would recommend air conditioning. I know from many years of experience that it can get really gross at night (and day) during the summer. I guess it's an individual thing, but like Dan (above), I just can't sleep if I'm too hot. I'm rarely a miserable person, rarely in a bad mood, but being too hot while trying to sleep is the best way to make me very unhappy!
PM me or email me (if you are also medicine and have access to the email addresses of the people in the intern class) if you have any comments/questions you'd like to share "off air."
Take care,
Priscilla