The area where your office is located is new. Apartments around them will be out of that price range. In the less than $700.00 a month range is going to put you in an apartment with possibly the more undesirable renters. Every apartment along Southside Boulevard gets bad reviews for noise, no parking, and lousy management. There were some apartments along Beach Boulevard that would be cheap but the reviews are too bad to recommend any. You might want to check with a professional apartment finder place such as:
Greater Jax Apartment Finder
8659 Baypine Rd
Jacksonville, FL 32256-7577
(904) 448-5920
Otherwise, I'd rent anywhere along Southside Boulevard or Baymeadows Road where the apartments are older but less expensive. You can't find reviews for some of these apartments because they have changed management and changed their names. Its a nice area, just old apartments. I looked up the rents on Southside, they are around $800.00 or more. One I found
http://www.chaseoaksapartments.com/floorplan.php
has awful reviews but was in your price range.