I also would suggest Port Aransas area parks. We researched them quite a bit this summer. The problem with these parks "on the beach" is beach access (believe it or not).
You can carry your stuff over the dunes on their boardwalks, but it's usually further than I want to drag stuff. If you want to drive, you'll find no access near most of the parks, except "On the Beach" and the owner of that place has a real attitude problem (check some of the reviews and his responses).
Of these, I think Gulf Waters is the nicest, and them there is Pioneer.
We ended up staying at Surfside RV resort in town, which was a 3 block drive to the beach and liked it a lot. No ocean view, but you won't have ocean view at the beach-side places either because of the dunes!
You can actually camp on the beach itself in the county parks, but I think you're limited to a max of 3 days (and it's boondocking).