I'll start with my favorite native sedge, Carex pensylvanica (Pennsylvania Sedge or Oak Sedge) It's native to Long Island and is found in partial shade to full shaded locations in dry to moist soil. Grows 6-12" tall. Mix with native Polystichum acrostichoides (Christmas Fern), Tiarella cordifolia (Foamflower), Iris cristata (Dwarf crested Iris and another of my all time fave natives), Chrysogonum virginianum (Green and Gold) and Heuchera americana 'Dale's Strain' (Foamy Bells). The dried foliage is used by birds as nesting material. Oak Sedge makes a great substitute for Asian Liriope muscari (Monkey Grass) and Ophiopogon japonicas (Dwarf lily turf).
My favorite native perennial is Pycnanthemum tenuifolium (Threadleaf Mountain Mint). It's native to Long Island and is found in dry to moist soils in full sun to partial shade. Native pollinators cover this fantastic nectar source with its tiny white flowers and purple specks from late June through September. The fine textured foliage ranges from 20-30" tall and mixes well with other native perennials like Echinacea purpurea (Purple Coneflower), Solidago species (Goldenrod), Heliopsis helianthoides (False Sunflower) and Monarda fistulosa (Wild Bergamot). Makes a great container plant and a fantastic cut flower.