We were in Rockport over the July 4th week and had a great time. Great fishing and eating (Boiling Pot). Caught the ferry to Mustang Island for the beach. Excellent!
Was trying to make reservations to some of the top hotels in rockport but it looks to be booked until school gets underway.
I grew up in Perth, and have lived in Houston, and now the Bay Area. I can reliably inform you that the only beaches that come close to Australian beaches are the Florida panhandle (Destin, etc). I took my family down to a place caled Capitola (south of Santa Cruz) and the weekend, after everybody raved about. Bitterly dissapointed.
Went to Gulf Shores, AL this year for spring break and can say that the beaches are pristine and the town is interesting. The drive is a bit far though.
6 of us (3 couples) rented a house in Rockport. Those four days only cost us (me and the wife) about $250. Add another $100 for groceries and you have a very inexpensive vacation. Its a very good blueprint for vacationing. We do this for our winter island vacations too.
We didn't know where to stay prior. My in-laws booked a Hawthorn Suites on S. Padre Island Dr. (mis-leading street name). It was solid with decent rooms and good breakfast, but it was in-town and a little ways from the beaches. I think staying near Mustang Island or Port Aransas would be better if you plan on spending more time at the beach.
Were you aware that Hawaii is one of the 50 US states? but yes, I love the Australian beaches! You guys have some great ones. I've only been to Bondi and the areas around the Gold Coast and thought they were very nice. regarding Texas beaches to the OP, just set your expectations low. The kids will have a good time regardless, even at East Beach or Stewart in Galveston.
Port Aransas. If you're looking for a reasonably priced place directly on the beach, check the Seaside Inn. It is not the nicest place in the world...but the rooms are clean and very reasonable for the location. We stayed there for at least the 10th time a few weeks ago. 1-bedroom condo was $189/night. We could have afforded nicer but the only point to the room was to have a place to sleep and eat breakfast.
if you want Caribbean quality beach, closest is pensacola and destin, FL, about 3.5 hours east of new orleans. look them up.