You have a lot of options, and all of them will do well in your area. I wouldn't try to grow grass under the trees-it generally does less well in shade. You could grow hostas and ferns, of course, and add almost any other shade-loving perennial to that mix. Some colorful flowering choices that also have good foliage are lungwort (Pulmonaria), spotted dead nettle (Lamium), ajuga (Ajuga), foam flower (Tiarella), toad lily (Tricyrtis), and astilbe. When planting, take care to avoid damage to the trees' roots as you dig, and do not add a layer of soil on top of the existing soil. Even a couple of inches of extra soil could suffocate some of the roots.