An easy and visually appealing art project to do with the golden ratio is to find the golden rectangles in famous architecture. You can find golden ratios and golden rectangles in the Great Pyramid of Giza, the Parthenon in Athens, the Chartres Cathedral, and in the 20th century buildings of architect Le Corbusier. You can find pictures of these and other famous buildings---with the proportions in the golden ratio superimposed on them---in art books and on the Internet.
Many famous painters throughout history have included the golden ratio in their paintings. Many painters choose to paint on canvases in the shape of the golden rectangle. Examples include the Holy Family by Michelangelo, the Crucifixion by Raphael, one of the self-portraits by Rembrandt, the Sacrament of the Last Supper by Salvador Dali, the Golden Section Plate 1, 1993 by Fletcher Cox, the Bathers by Seurat, Composition with Gray and Light Brown and Composition in Red, Yellow, and Blue by Piet Mondrian. Discovering golden ratios in famous paintings is an interesting art project.
Leonardo Da Vinci used the golden ratio in almost all of his paintings. In the painting An Old Man the face of an old man is drawn in a series of golden rectangles---one for each feature of the old man. In the Vetruvian Man there are three golden rectangles framing the head, the torso, and the legs. In the Mona Lisa there are many golden rectangles and there are golden ratios galore in the ratios of he distances between focal points of the painting. Take a ruler and a calculator to a reproduction of almost any Da Vinci painting and you will see the golden ratio everywhere.