I live in Corpus Christi. March tends to be windy which means days of 20+mph CONSTANT wind with gusts to over 40. Not everyday, but be prepared (don't leave out awnings or furniture). When I owned a house my elderly neighbors tended not to go outside on those days.
One doesn't need A/C fulltime usually until late April. Temps may not be all that high, but humidity is always significant. I use a dehumidifier year-round as the A/C works less and keeping the interior at 40-50% takes out the damp of cool mornings and relieves mid-day stickiness. Also warms the interior slightly. (A rolling floor model a little under $200).
Year-round this city is always more pleasant in the evenings. Use the early day to do shopping or whatnot. Plan an early return to enjoy a fine meal. I try to finish up any running around by 3pm to use remaining daylight outdoors.
Rockport is an hour away and in some ways prettier as the parks here are limited in number. It's always a longer drive to anywhere, but the accommodations might make the difference for you.
The Valley is a world of its own. The place you recognize as the U.S. ends here at CC. From here south you are in Texas, but . . . . ( I also work all over South Texas.)
The Hill Country is very attractive, but far enough north (about 150-200 miles) to still be pretty cool overall, and especially at night. There are next to no good restaurants south of San Antonio (if one compares to what is available in Dallas or Houston, cheap or expensive) so the Hill Country with access to SA and Austin makes for better day trips.
Of RV parks in Corpus Christi I would say the nicest one is Colonia Del Rey. Excellent location as the city and the Island are both an easy drive. The Island is always windy (great in the heat) so you might want to stay inland first and check those parks before moving to one. Also, lots of sand. I won't take my TT to the island, FWIW. That said, the National Seashore is very nice.
Good luck.