Between all the digging and running your dog puts in, lawns take a beating.
Plant hard-to-kill grasses commonly used on sports fields.
If you have a large yard, think about putting in a wildflower meadow area. The combination of hardy perennials and grasses will give your pup a wonderful place to frolic and the free-and-easy growth habits of a natural landscape disguise damage from trampling better than neat rows of single-species shrubs or flowers. Use hard surfacing like flagstone or concrete pavers to reduce the necessity for greenery in paths your dog frequents, and put super-tough ground covers.
Always research any flowers and other landscape design plants before putting them in your yard to ensure they do not pose a poisoning hazard to dogs who like to sample the vegetation.