Going Crazy!

We are trying to find an apartment to move into in a few weeks and we can NOT find anything! I have searched every newspaper and online listing that I can find and can't find anything that fits our needs. We are looking everywhere from Draper/Riverton all the way up to Layton. We really need to stay at less than $750 with utilities. We need 2 bedrooms and washer/dryer hookups. And we don't want to live in West Valley or Rosepark! If you know this area, that is self explanatory! :) There are tons of listings that fit this need, and I am checking them several times a day, but by the time I get through to the lister, the property is already rented. Or they find out that we have two kids and tell me that they are not accepting applicants with kids. OR we call them and find out that the apartment is really just an open basement with shared kitchen and living room areas!!! WHAT?!!! Why would I feel safe moving into a house with a family that I don't know, sharing a house with only separate bedrooms. And what is to stop their kids from running into my bedroom in the middle of the night? Or to stop one of the adults from going into my kids' room at night? Sorry. Too scary for me. I'm really not too picky. I don't care if it is old and dumpy, as long as I can clean the carpets and there aren't roaches, I'm good. So, if anyone out there knows of anyone renting a basement apartment for less than $750 with utilities anywhere in the Salt Lake valley (except the REALLY scary areas!), let me know! Please! :)