You can let the housing person at your company know what your absolute requirements are in a place (safe area, etc.) and what your preferences would be. If you are flexible on some, for instance distance from the hospital you are more likely to get others.
For example - I need a first floor apartment as my mother visits during most contracts and an 83 y.o. has trouble doing stairs. Thats a must. I've told them that I will accept a nonsmoking apt. even though I smoke as long as it has an outdoor space - patio or balcony where I can indulge. On this next contract, since it is in an area of extreme summer heat, I'd really like a facility with a pool. That's a preference but not a demand. I've told them I am willing to drive a bit further to work if they can find a place that accomodates all this.
Know that what constitutes good housing in some area may not be what you are accustomed to in other areas of the country. For example a single wide trailer might be good housing on some reservation contracts.
Negotiation is the key - give and take. And by all means keep it friendly and nonadversarial with the housing person - they will remember it the next time and can really do nice things if you have established your rapport with them. (That's how I ended up in a private house with it's own inground pool on one contract!)
Edited to add: You really can try to negotiate almost anything. I have a friend who actually had written into her contract (because the recruiter had a sense of humor) "No baby-poop green couch". It's one of the standard Cort Furniture rental furniture colors that shows up way too often!