sjarrell... There is a lot to see and visit along your proposed route and as you probably know your task is to find the quality sights and highlights of the areas you visit. Not knowing what your interest is... I will give you some suggestions that I think will make the most of your time.
It appears that you have dropped Brownsville from your trip. I think that is a good move given the time frame you will have. Save that for the next trip... don't know what to advise you to see there except South Padre Island and border crossing into Mexico, if you must.
Do try to include Kema, Texas and its boardwalk (water view but no beach at this location). Good restaurents (Aquarium Restaurent) and clean amusement park atmosphere. Galveston has the attractions Jim Gratz mentioned, plus a waterpark (Schlitterbaun ..sp). I have not been to this relatively new waterpark... however its sister location in New Braunsfeld, Texas (I-35 between San Antonio and Austin) is quite popular and located in a German settled communityl
If you are interested in history the San Jacinto Battleground and USS Texas (WWII battleship) are located near Kema and could be included in a two day visit. The battleground is the location where Sam Houston and the Texan Army defeated the Mexican Army and Santa Anna to establish the Republic of Texas.
Take US Hwy 59 to Victoria and cut across to Hwy 35 and travel to Rockport/Fulton. From there travel to Port Aransas and ride the free ferry to Port Aransas which is located on Mustang Island. Look for Dolphins playing along and in front of the ferry while crossing the waterway. The University of Texas Marine Science Institute has a museum here and would be worth the time to visit. Since you are not going to South Padre Island, this is the beach to visit. You can drive the island road from Port Aransas to Corpus Christi and the Padre Island National Seashore. You and tow the road... but avoid going onto the beach with your rig. I have seen some on the beach near the access road and they seem ok, but have also seen some stuck along with the wrecker/tow truck.
Include my original hometown of Corpus Christi (Sparkling City by the Sea). Drive to the bayfront and park on the "T"-Head or one of the "L"-Heads and walk the seawall. At the northend of of the bayfront is an interesting museum with relics from early Spanish explorers to this area. The WWII aircraft carrier USS Lexington is now a museum on North Beach and also worth a visit. I believe a replica of one of Christopher Columbus' ships is still moorned near-by (built in Spain and sailed to America some 20+years ago).
Do try to have time for San Antonio,,,Alamo, Riverwalk and I-Max presentation about the Battle of the Alamo, all located downtown and in walking distance of each other. Make this a whole day to include evening meal along the Riverwalk. Sea World is located on northwest side of San Antonio (might have to check if still open when you make trip). If still interested in waterpark at New Braunsful... travel east on I-35 .
These would be some of my highlights. Much more if you have time. Bracketville and the movie set of John Wayne's movie "The Alamo", Big Bend, Garner State Park (camping rite of passage for many Texans growing up).
Sorry for length... but if you come to Texas we want you to have a good time while we show off.
Jerry