Very much the wrong time of year for Whoopers. They are in the area in the winter months, like Dec to Feb. There are boats that come out of Port Aransas and do the Whooping Crane Tours. They actually have a Whooping Crane Festival in Port Aransas in Feb.
What you are going to get are shorebirds and migrants flying back through. Very hot time of the year any where in Texas!
In Corpus Christi, you could bird Blucher Park, Packery Channel County Park, Port Aransas, Pollywog Ponds, Hazel Bazemore (hawk watch may or may not be started by then), Hans A. Suter Wildlife Area. On Port Aransas proper, you can bird the beaches, Paradise Pond, Leona Turnbull Birding Center, Charley's Pasture (kind of behind the birding center) & Mustang Island. The Padre Island National Seashore is an option too.
If you are game and had the time, you could zip down to the valley (2 hrs approx, depending on where you decide to go) and pick up some valley summer specialties.
There is also Rockport - they have a Sept hummingbird festival - not sure what can be found in August. Choke Canyon is about an 1 1/2 away, heading towards San Antonio, if you had the time. Calliham Unit would be good there.
If you are on Ebird, you could check the areas you are interested in to see what others are reporting & what was seen in the area in August of last year.