An inexpensive ground cover that adds nitrogen to your soil every time you cut it is clover. But since you are doing a lot of grass you may want to keep it away from your lawn if you're picky.
Thyme is good for a drought tolerant ground cover and quite aromatic.
There are many wonderful creeping types of sedums that form dense mats only 3 inches tall. With succulent leaves and stems, sedums can thrive in low-water situations, and they bloom in shades of white, pink, red, purple, yellow, or orange, depending on the variety. Sedums are prized for use in green roofs and living walls because they are so adaptable.
Hens-and-chicks makes a terrific groundcover in tight spaces, such as between paving stones or in a trough. The plant is also a beautiful textured focal point in a sunny garden. The succulent rosettes grow 3-6 inches tall. They're easy to grow, and need almost no maintenance.
Try one of the many varieties of ajuga where grass won't easily grow. It can take a bit of foot traffic, but avoid growing it in areas with a lot of activity. Flower spikes in blue, pink, lavender, or white adorn the rosettes formed from scallop-shape leaves in spring. Grow this tidy groundcover plant for its pretty leaves, which come in shades of green, maroon, bronze, purple, pink, or white.
As tough as its common name, brass buttons grows no taller than 3 inches with textured, feathery foliage in shades of bronze-black to purple-gray and small, buttonlike yellow-green blooms in late spring and early summer. This versatile New Zealand groundcover plant grows in full sun to partial shade and moist but well-drained soil.
I would be careful planting deer plot seed as ground cover unless you want the deer to eat it!
