Davy Crockett is certainly convenient for those quick trips when you've got cabin fever and just have to get out there, but it's fairly flat and heavily wooded, so there's not much of a view. On top of that, the USFS recommends not to drink the water, even filtered. Too much ranch runoff I guess. There are, however, several places to cache water.
I haven't done anything overnight in OK, but I really like Caney Creek Wilderness in SE AR. Anywhere along the Ouachita Trail or the Albert Pike area would probably serve you well, I just can't vouch for them personally as I haven't been. I keep meaning to get to Eagle Rock Loop, which passes through Albert Pike, but something comes up every year.
If you want something closer to home, Dinosaur Valley SP is beautiful and has nice trails. I think it's even got water this year
. I haven't done an overnight there either, and I'm not sure how long the back trails are, but you could always take them slow and enjoy the view more to make it a 2 night trip. Stop and "smell the roses" often.
Lost Maples is sort of in the same category - convenient (though not as close as DVSP), gorgeous, somewhat small. It's one of my favorite places for day hiking or just hanging out.
And finally, if you want to go out west a ways, I hear Guadalupe Mountains National Park (GUMO) is amazing. Only thing there is you have to pack all your water. It's scarce if present at all, so they ask you to leave it for wildlife, and there's nowhere to cache it.