Here is the surf fishing bible:
https://texags.com/forums/34/topics/2857318Might need a 4x4 to be able to do it right and move until you find a bite. Without 4x4 I couldn't even get onto PINS first weekend of June and every other beach I checked was too crowded to fish very well, ended up in a small opening off access rd 3. I didn't try Mustang Island SP, need to next time. Probably doable if you are just going to fish early and leave/switch to beaching when the crowds show up though, I was on my kayak for the morning fish.
I mostly Kayak fish and dabble in some surf fishing, but if a bit of shallow wading is acceptable, I normally see people fishing near the launch points. Bird Island Basin (NW of the small parking lot loop, not the campground), Kates Hole/Corpus Pass Launch Point, north side of Fish Pass **, Wilsons Cut. There is also the JFK Causeway access road between Red Dot and Snoopys, I've never actually fished there but man the water looked good the last time I drove through.
** This "road" in particular can get real hairy with rain or high tides. If you are going on any of these roads though, be aware of the time and strength of the tides. Current google satellite looks like it was taken at a low tide, for example the last time I was at Wilsons Cut the channel where the boat ramp pin is was 3' deep.
As for methods, my favorite is a weedless spoon in the < 3' flats. Also, toss a Carolina rig with a hunk of fresh cut mullet into a sandy spot in some grass. Don't soak the mullet before you cast it out, you want all those oils on there to attract the fish. A paddle tail shad or trout assassin at a drop off, anything under a popping cork would probably work here as well.
Other than that, I will say that if you do end up pier fishing get a hand full of two ring crab nets at Academy and some chicken necks from HEB.