'longs to do' is a correct and usable phrase in written English.
It is typically used to express a strong desire for doing something. For example, "Samantha longs to visit Paris someday."
Clair-de-Lune cannot speak but longs to do so.
In these four small illustrations, the child himself is doing what anyone young longs to do in a museum -- touch!
She, unequivocally, is Jo, the fearless girl (and aspiring writer) who longs "to do daring things", and who struggles to escape the Victorian prison of her gender.
Hollywood has been interested in "The Secret Life of Walter Mitty" since Thurber's story was first published: the idea of a timid man who longs to do momentous things is an extraordinarily relatable one.
Here are songs that capture urban vitality, dissonance and ambition in a way that "Sweet Smell of Success," the newly opened Broadway musical, longs to do but never manages.
At one point, Theseus says that he's tired of trying to please audiences and producers, and longs to do more meaningful work; Dendy has said that, while his work on and off Broadway ("The Pirate Queen," "Taboo," "The Wild Party") — and even a brief stint choreographing for the Rockettes — was valuable, he wanted to get back to something more personal.
