Actually I live right across the street from Jamestown. The units themselves are nice and most were renovated within the last few years; they're mostly 2 story colonial-style townhomes built in the late '60's. The grounds seem well-kept and nicely landscaped as well. However over the years the quality of tenants there has seemed to deteriorate somewhat and the units that are on my street (the garden apartments) haven't been updated like the rest and seem somewhat "dumpy." Not to mention like mdawg stated most of what I've heard about Jamestown seems negative, namely poor management. The place isn't really a dump or "ghetto," its just that there are better choices.
If you must live in a large suburban complex then as stx stated I'd go with Waterford Place, Cypress Pointe or Mallard Crossing which are also off Breckenridge along Kresge Way/Bowling Blvd (the road that runs by Baptist East Hospital). Any of these would be a fine choice, with Waterford and Mallard being the nicer two. They both have very nice grounds and units (both have a nice lake area and a creek runs through part of Mallard) and are right across from Brown Park, a nice wooded park with several walking trails; not to mention they're 3-5 minutes from Mall St. Matthews. If age matters Waterford and Cypress were built in the early '80's, Mallard in the early '90's.
I'm not as familiar with Stone Mill Village but I do know that its off Westport Rd in Lyndon, which is overall a good area and the complex seems nice-I'd probably pick it over Jamestown.
http://www.mallardcrossingapartments...SKY/index.aspx