Mow and cover what you don't want. But I certainly wouldn't get rid of all (or even most of the nettles). Nettles is a most excellent plant, it has the highest protein of all plants. To us, it would be odd to get rid of nettles so you could plant a garden. Nettles is the garden. Its also good medicine. For example, yesterday one of the women here had a tooth ache. She took fresh nettles and "whipped" them across her face. It stung a little bit at first, but then its "medicine" kicked in and the tooth ache went away. Its a good temporary solution till getting to the dentist.
Another consideration is a discussion on another forum. Someone asked about getting ready for some sort of catastrophe. Replies mostly spoke of storing food, guns, medicine and such. Something I didn't notice was any talk about "the edible landscape". If we ever have a real economic/social/biologic meltdown, folks will be hungry. Your "traditional" garden of tomatoes and cabbage may quickly get eaten by the neighbors/trespassers. But very few people will know to take/eat your Jerusalem artichokes, comfrey, elderberries, may apples,
locust pods,
dandelions, nettles, etc. You'll still eat. Others, less knowledgeable and prepared, will not.