Finding an affordable place in North Shore or downtown?

I am relocating soon (without much warning) for my job. I had the opportunity to spend 3 days in Chattanooga and get a feel for the area. I love downtown and North Shore, however, have not been able to find a affordable place. I am looking in the 600-700 dollar range and would like to be within walking distance of the area. I have been given leads from real estate agents on areas in the outskirts, supposedly in "prime" areas, which I wouldn't even dream of parking my car at in my worst nightmare. So any help or advice, even condos being rented I'd appreciate because I'm lost.