rockhill

Palo Duro in July would be a little tough. Hot, dry, windy. Not much around Carlsbad for shady camping.
i would vote for Davis moutains for a couple days, a little cooler and you could day trip to Balmorea for a cool dip in the springs/pool. While at Davis you could do the observatory and the old Fort for contrast. I would then come back to Frio canyon. Slower pace on the river compared to Guadalupe and if Garner is full, a lot of other camping choices to pick from. Of course it will be hot there, but the Frio will still be cold. Not many places to take a dip/float/get cool around Palo Duro.
Just one persons opinion, yours may differ. I suspect you will have a good time either way.