Personally, I would skip Texas and head a bit further north, through Colorado and Utah. Utah has some amazing national Parks, such as Arches, Canyonlands, Zion, Capitol Reef, and Bryce Canyon. The mountains of colorado are amazing. After Utah you could head south to the Grand canyon, and then across to Nevada and california.
I think you've got too many cities on your route....most American cities are not really all that great, and el Paso has to be one of the worst of all.
If you must go through west Texas then make sure you go to Carlsbad caverns, just inside New Mexico. Phoenix is OK but northern Arizona is much nicer (someone mentioned Sedona....nice place and Oak Creek Canyon just north is great too).
think about austin and new orleans along the way.
Savannah is beautiful! Take a walk along the river... There are a few really great candy shops and some really neat stores... I was born in El Paso and I am not going to lie... There isn't a whole lot to do...
Organ Pipe & Saguaro Nat'l Parks and the Sonoran Desert Nat'l Monument are close to Tucson and worth your time. Not many places have the abundance of cacti that makes southern AZ unique.
My suggestions of cities deserving of a visit: Washington, DC (if you are interested at all in US History,e tc.), Charleston, SC., St. Agustine, FL, New Orleans, LA, Memphis, TN, Hot Springs, AR, San Antonio, TX, Santa Fe, Taos or Albuquerque, NM, Tombstone, Sedona and Grand Canyon, AZ, Death Valley, CA, the canyon lands of southern Utah, Durango, CO.
Just my thoughts.
Hope you have a great time.
I'd skip most of the Texas stops - after a little, it all kinda blends together there. Like somebody said previously, you might want to dip up into the rockies. I wrote a little travel blog about a cross-country trip from the northeast through memphis, then dipping up into Santa Fe, Telluride, down through Monument Valley, the Grand Canyon, and finally through the desert to Orange County. I've driven cross-country 13 times and this is a route I've kinda developed to keep it interesting and to see the best range of the US - http://www.wuts-happening.com/whutshappening/2008/01/cross-country-w.html If you want to follow the whole trip, just click on the roadtrips tab on the side for the next blog posts of the trip. Hopefully it'll give you some good ideas. Good luck.
San Diego for sure yeah. The others I couldn't really say.