You can fill jugs for free (donations accepted) on the east side of the Coyote Corner gift shop. The shop is on the east side of Park Blvd (across from the park visitor center) in downtown JT.
Thanks for all the answers! I found there is free water fill at the Oasis Visitor Center during operating hours. There is a 3 minute time limit on filling.
We were able to fill up jugs at the national park campground, although they wouldn't let us fill up our rig if we weren't staying there. Other than that I don't think there is a free option.