Texas Gulf Coast in April

SpeakEasy wrote:
Starting to put together some loose plans for this upcoming April. It's just the two of us; newly retired; wanting a starting taste of an RV lifestyle. We've done a lot of 2 to 3 week trips around the eastern US and some to the Rockies. Now we'll be setting out on a 6-week adventure to the South. I'm thinking some of our time should be in the Gulf Coast area of Texas.

I want to try this without a completely tight schedule, so probably no reservations. We prefer state and national parks, as well as some municipal parks, rather than RV resorts. We tend to like COE and BLM campgrounds too. We like a mix of dry camping and hookups. We like nature and wildlife. We like to see local "attractions" where history happened. We like scenic drives, some low-impact hiking, and just hanging out in the quiet of a natural setting. We like factory tours, museums, and the arts as well.

Here are my questions about Texas:
1. Along the Gulf Coast, what are the two or three spots not to be missed?
2. Where are the areas that are not likely to be back up and running after the hurricane?
3. What's the weather likely to be like in April?
4. Any places I should totally avoid because of "Spring Break" activity?

Thanks!
-Speak