Matagorda Bay is a neat beachside park, a fairly new park, really nice conrete sites, with lots of palm trees throughout the park. It's a LCRA park with a similar atmosphere as a nice State Park. The sites have both 30/50 amp electrical service, sewer connections and a picnic table. The park also has a really interesting Nature Center with exhibits, a small store, a canoe rental facility, a coin-operated laundry room and bathrooms with showers located conveniently right in the middle of the campground. The park is approximately a 10 minute drive south of Matagorda, TX. The small town has a couple of great seafood restaurants as well.
When we visited last year the beach was really clean with tons of great shells (if you're into collecting shells) and the water actually looked nice. The only word of caution is that there are rattlesnakes along the waterfront sites where the Colorado River feeds into the Gulf of Mexico. So watch where you walk along the river.
Matagorda Bay Nature Park
I would estimate it to be approximately a 4 - 5 hour drive south of the Dallas metroplex.