If you don't want grass there are other options besides plastic. You can grow herb lawns, corsican mint and penny royal both work. Or some big shade trees will reduce the length that the grass can grow.
Lawn is pretty bad for the environment and fake lawn isn't much better so a lawn free garden is great from an eco perspective. You can have lots of trees with paths, rock gardens, ponds...
ETA - check out the
Australian Native Plants Society for some idea about what you could do without using lawn.