I'm not sure which state park, but I wouldn't worry too much about breaking down your campsite just to go for a day hike. If you have valuables, either take them with you or lock them in the vehicle.
Water. We did a lot of summer camping in central TX. Not sure about the availability of water, but I always packed along two smaller (2.5 gallon) Scepter water cans. They're smaller than the 5 gallon sizes and easier to transport. Your gallon jugs will work fine, just make sure you have enough for drinking, cooking, coffee, and hygiene. In your temps, a gallon a day is probably okay if you're not over-exerting yourself.
Part of your FAK should include sun screen and bug repellent.
Not sure how far you plan on hiking, but some trail snacks (trail mix, granola bars, etc.) are nice to have on hand.
If you have a spot to hang a hammock, an inexpensive hammock (like ENO) is an excellent "lounge" chair for the campsite. It's also a great place to lay down to read or nap and excellent for really hot weather.
Lastly, take a notebook and pen/pencil. Identify what was most useful/used, what wasn't really necessary, and what you should have packed. Your own personal Lessons Learned to make the next trip better. After years of camping and hiking, I still make a checklist/packing list. Life always makes you too busy to pay full attention and it's ironic how easy it is to forget the most basic and essential item.
ROCK6