acariciar

To caress or stroke — used for physical touch (acariciar el pelo de alguien) and, figuratively, for a hope or idea you're fondly entertaining: acariciar la idea de mudarse. Common in both tender and reflective contexts.

• Acarició al gato mientras leía. — She stroked the cat while she read.
• El viento acariciaba las hojas de los árboles. — The wind caressed the leaves of the trees.
• Llevaba años acariciando la idea de escribir un libro. — He'd spent years entertaining the idea of writing a book.

Learners sometimes use tocar (to touch) where acariciar's gentleness is the whole point — tocar is neutral contact, acariciar specifically implies a tender, affectionate touch.