First, I would not consider Clarksville a suburb at least by a "Tennessee" defintion (ie non-So Cal definition). Clarksville is not really considered a suburb, but I guess one could call it an exurb. Many people do commute from Clarksville to Nashville.
As far as school systems, usually the schools in the suburbs nearest Nashville in the collar counties are considered the best: Brentwood, Franklin, Mt. Juliet & Hendersonville. Williamson County (Brentwood & Franklin) schools are considered the best. Many love Williamson County while others hate the cookie cutter suburban vibe they perceive of it. Home prices have shot up in Williamson County and people have gone further south in the county to Thompson's Station and Spring Hill (part of it is in Maury County.....Maury is pronounced like Murray so if you say Maury like Maury Povich, then you ain't from around here are ya?)
I would take a look at the Murfreesboro area in Rutherford County in addition to other areas. You can hop on I-24 and in a couple of hours you can kayak outside of Chattanooga. Take I-840 to I-65 and in 2-3 hours, you are in the Smokey Mountains. It is growing town that is now more than a college town (Middle Tennessee State University) and I think its schools are considered pretty good.
If you want elevation, try Monteagle,Tennessee.
About the weather, one reason that between LA and San Diego there is not much land left to develop is that it stays between 60-80 degrees most of the year. You are just not going to get that in Tennessee. Tennessee has hot summers and mild winters plus, there is humidity here. Check weather.com for the monthly averages in the Nashville area if you have not done so already.
Middle Tennessee has friendly people. Nashville is growing with people coming from all over, but it retains its Southern cultural core for now. If it keeps growing, then it might become another Atlanta (let's hope not, but.....). You'll get taxed at 9.25% when you shop, but you will not see a state income tax on your paycheck.
The obvious advice is to visit the areas you are considering. While in this area, you can stop by and see the Nissan HQ (more Californians!
) being built in Franklin across from Cool Springs Mall.
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Ca family checking out Clarksville
nearby close, we love being near the mountains, don't mind the rain to get all the green that the Southeast provides, love the seasons! Need a growing economy for Daddy to work. We were narrowing it down to a suburb of Louisville, Kentucky in Oldham County which is beautiful, but I still haven't really found "that town" that I am looking for. 
Obviously subjective, but any points in the right direction will be much appreciated!! A area that is also known for great value and low cost of living would of course be very beneficial. Will be buying a home outright in the $250K zone [or below] and want to be able to get at least a 3+ 2+ 2200 sq ft or bigger on maybe a 1/2 acre or more? 
Trying to find a area that might be a bit milder in weather for both the summer and winter since were kind of spoiled coming from So. Cal. Like a little elevation to help that out. Have done all the Top 25 or 50 location finders from various sites, so now I am taking it to the people! Tell me what you like and why? This forum has been fantastic for me with my previous research, so I am posting this same request on multiple locations that I have narrowed down from our criteria. Thank you in advance!
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