Andy Griffith Museum -- 'We are Brokenhearted'

The people who run the Andy Griffith Museum in his birthplace of Mount Airy, North Carolina tell TMZ they are "brokenhearted" over the death of the TV icon ... saying "We are blessed to have known him."

Tanya Jones -- the Executive Director of the Surry Arts Council -- also oversees the AGM ... which contains the largest collection of Andy Griffith memorabilia in the world.

Jones tells us, "Andy Griffith means the world to the arts everywhere -- not just here in Mt. Airy. His contribution to us, the Surry Arts Council, and the town of Mount Airy cannot be measured."

She adds, "We are blessed to have known him. We will cherish his art, his music, his talent, and of course, our beloved Andy Griffith Show."

"Our prayers and love go out to Cindi. We know that Andy is at peace and that is what is important right now."