There are multiple ways:
First off, you need to contact your hospital/program, because they have people coming in for short stays all the time so they know the best places.
Look on craigslist, there is a sections called subletting/temporary housing
Look for Extended Stay brand of hotels. Usually very reasonably priced and their rooms are like a studio apartments with stove, fridge and they even provide plates, bowl coffee maker, toaster pots and pans.
If you do the hotel route, use priceline name your own price, just make sure you choose an area you like. I have used Priceline and have saved anywhere from 30-100 bucks a night
Another way is to look for short term stay apartment/houses that cater to businessmen. They are usually cheaper than hotels but more expensive than the sublets.
