Hey Crotty,
I'm sorry for the delay, I completely forgot that I had posted here until this afternoon. It's not a board I frequent very often, so I hope this response isn't too late to be helpful to you.
The south side of the city is definitely the better side, and there are some very nice neighborhoods, with some pretty affordable living. One of the best parts of living in Lexington is that you're never far from the country. From wherever you are in the city, you can be surrounded by horse farms within 10 minutes of driving time.
Some of the best houses for the dollar are going to be in a neighborhood on the northwest side of the city called Masterson Station. I have a few friends who live there, some with elementary aged children and I never heard them complain about the area. The houses are pretty new and nice, But there are some definite drawbacks, like the relative proximity to some prisons just to the west, as well as some less than stellar areas of town not too far to the south and east. So those would certainly be some concerns that a Realtor might not mention while showing you a nice house in the neighborhood.
I don't have children, so I don't know much about the Lexington school system, but I know that the Beaumont area in the southwestern part of Lexington is known for having some of the best schools in the city, which funnel into Dunbar High, which is pretty well regarded academically (I can say that Dunbar is quite disproportionately represented in UK Law's student body). But that is a pretty expensive part of town. The Veterans Park neighborhood and surrounding area in south central Lexington is also supposed to have some high quality schools, and should be a good bit less expensive than Beaumont while still being a very nice, family friendly part of town.
I lived in an apartment in south central Lexington near the intersection of Man O War and Tates Creek, and I loved it. Tates Creek is a relatively easy route to get to and from UK/Downtown, there are nice parks nearby, a nice Kroger that is currently being expanded into a much larger Kroger (should be done soon from how it looked when I was there a couple weeks ago), and you are very close to a lot of good restaurants, stores (Wal-Mart, Lowes, etc. as well as the Fayette Mall which has normal mall stores like Macy's), and good access to the rest of the city between Tates Creek, Man O War, and Nicholasville roads.
Commuting on Nicholasville Road during peak hours will take a toll on you. It can take a very long time to travel even a modest distance and the direction of the lanes change with the traffic flow (more lanes towards downtown in the morning and away from it in the evening) which can be harrowing in and of itself, so try to avoid that if you can. Smaller roads like Tates Creek and Alumni are much less stressful commutes from the southern side of the city, and are usually much faster as well.
If you really want to avoid suburban living, Nicholasville is just south of the Fayette county line, not really much further out than Veterans Park area and you certainly won't have to worry about looking into your neighbors windows as minimum lot sizes are much larger once you cross into Jessemine County. And there is some new development down there as well, with grocery store, restaurants, movie theater etc. so you wouldn't really have to drive any further to a grocery than you would on the Lexington side. I have no idea what Jessemine County schools are like, but it might at least be an option to explore with a Realtor.
Really it's hard to go wrong on the south side. The area known as Woodhill in the southeast can be a little rough, but other than that, you'd be hard pressed to find a bad area anywhere along Man O War Boulevard.
I hope I was able to give some insight. I'm sorry I don't know more about the schools, but I hope I was still helpful to you. I hope you get to go to Lexington, it really is a great place to live. Friendly people, nice slow pace of life, and overall just a pleasant place. I would go back in a heartbeat if a job opportunity came along. Best of luck, and let me know if you have any other questions, I'll try not to wait 2 weeks to respond.
This might be a useful tool for you. Not sure how credible the website is, but you can view and compare the elementary schools in the city which are rated on a 1-10 scale, and see them laid out on a map of the city, kind of a nifty thing:
http://www.greatschools.org/kentucky/lexington/schools/?view=map&pageSize=100&gradeLevels=e&st=public[This message has been edited by GregZeppelin (edited 10/29/2013 1:21a).]