There aren't many herbs that will grow in low light.* For hanging baskets in part sun consider Angelica, Catnip, Chervil, Chives, Lemon Balm, sweet Marjoram, Oregano, Parsley, Peppermint, Spearmint and Sweet woodruff.
For something else different I like Torenia aka Wishbone flower.
Nasturtium will grow in part sun and is edible.* Fuschia is another that likes part sun.* The triphylla varieties are more upright.* I like them and grow Fuchsia 'Gartenmeister Bonstedt'.* Here's pic of a very mature plant.* I overwinter mine indoors as it's not hardy in my zone 7 garden and I can't always find it every year.
This UK site has lots of Fuchsias to drool over.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.