I suggested two backpackers that are the closest possible to the hospital.

The apartments in town in Christchurch are not like in Auckland, they are mostly for rich people who are residents... even though YMCA across from the hospital does offer student accommodation.

I would suggest looking at the suburb of Riccarton, which is close so you can even walk to the hospital, through Hagley Park, or bike, Christchurch is flat as so it wouldn't be a problem.

Students in Christchurch generally also flat around Ilam, but even though that's close to where I live, it's further from the city centre.

If you're trying to find a place for yourself,... I would say around 200 would get you a nice furnished place, but I'm not too sure.

Here's a place that's the closest to the hospital that I could find, that is not too expensive:
http://www.trademe.co.nz/Trade-me-property/Residential-property/Houses-to-rent/auction-250480829.htm

Probably you could live in a unit in a house for a year, than start flatting with new friends, especially if you start driving, you'll be able to find cheaper places. Though, like everywhere else, parking in the city centre can be hard...

Well, here are all I can offer you at the moment, I wish you luck, honey!!