Singletree Falls and Lower Calf Creek Falls UT -- May 1st

I was there in April. As IA_boy said, the parking lot is only about 20 cars. There is a campground there but I didn't look to see large the sites were -- most of the people were using tents.

We stayed in Escalante. There's a newer park in town next to the Grand Staircase National Monument information center. There really is a lot to do in this area, you could easily spend 3-4 days there. Kodachrome basin is nearby, some great dirt roads.