Kerrville Folk Festival starts late May and runs to early June. There are small events during the week but they get some great singer/songwriter acts on the weekends. Peter, Paul and Mary have done performances there and are very involved. One of Mary's last performances was just a few years ago before she passed. They get acts from all over - one of our favorites was a traditional violinist from Ireland, and Trout Fishing in America is there every other year or so.
There is also a small wine and music festival in early September. We've never been to that one though.