Before planting creeping jenny, check with your local extension office to be sure that it is not restricted in your area due to its invasive nature. Creeping jenny is a hardy plant that will thrive in full sun or shade.Purchase plants from nurseries in the spring and choose a site, in the shade or sun that drains well.efore planting creeping jenny, check with your local extension office to be sure that it is not restricted in your area due to its invasive nature. Creeping jenny is a hardy plant that will thrive in full sun or shade.