Diamond Fork

The best place to car camp for free is at the Dry Canyon Campground about a mile below the trail head. It is also getting busier. There are about 6 sites with picnic tables and fire pits, but no water. There is also a latrine. You have to cross a nice foot bridge and walk into the sites. So a wheelbarrow is nice to haul gear. If the established sites are filled up, take a right after crossing the bridge and there are a couple places along the river that you could camp with just rock fire rings. There is also one small place above the other sites up on the right.

Go southeast of Spanish Fork on highway 6 until you see the Diamond Fork turnoff on the left. There is a nice pay campground not far up the road that costs $24. They now require reservations. See information at https://www.fs.usda.gov/recarea/uwcnf/recreation/camping-cabins/recarea/?recid=9855&actid=29 . In the summer there is a shuttle to the trail head from here. Continue on a few miles if you want to camp at dry canyon.

I would suggest that you hike in very early Saturday morning and avoid the crowds and avoid the springs on Friday nights as well, due to the skinny dippers and drinking crowds. It is an easy 2.5 mile hike to the springs. Go straight up from the trail head; don't turn right over the footbridge. There are a few nice places to camp along the trail below the springs, the better one being closer to the springs. Be aware that people are hiking up and down the trail all night. I've heard that there are places to camp further up as well and that you can also hike down to the springs from a higher trial head. See http://www.utah.com/hike/fifth-water-waterfalls-and-hot-spring-trail for more information. There are multiple springs spread out over about 1/4 mile. Some of them are a little too hot, but are probably cooler in the spring when there is more water flow. It's also fun to sit under the water fall shown top left. There is also a good place a little ways above the waterfall.