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We are planning on spending a week in the hill country (staying in Fredericksburg) in about a month, and Llano is on the list of towns to visit, so I can't answer your question now, but may be able to at the end of May.
There is a nice city park in Llano - 12 sites arranged in an asphalt parking lot beside the City Park. The park is nice, right along the river bank, but the RV area has no shade. 100 W. Burnet St Latitude N 30.75442 Longitude W 98.67680