Never stayd there but found this online: Seabee Park at Fort Phantom Hill Lake (City Park). Directions: Take I-20 exit 286C. Go north on FM-600 for about 3.2 mi; turn right (East) onto Seabee Park Rd. Continue on paved road for 0.7 miles.
Website says you can stay 48 hours. Free. There is another free campground on the same lake but farther from the highway.
Texas also allows overnight parking at their rest areas (one night only).
Rest areas are at miles markers 256 and 296 on I-20 near Abilene.