Buy a Mower
Again and again I read about well meaning people saying, “If you get a goat, you won’t have to mow your lawn”. Here’s a news flash for you: the goats won’t mow your grass.
Goats browse. They aren’t cattle or sheep, they don’t graze and they won’t vacuum up all that pesky grass in your yard. They’ll eat your bushes and roses and trees and most of the weeds. The ones they like. And your flowers.
The only way you’re going to get a goat to keep your grass down is to tie it in one place until it runs out of yummy stuff and is forced to eat the grass. Then you’ll have to move it. You’ll wind up with crop circles in your yard by the time you’re done but, yes, it’ll keep your grass short.
Goats are great at clearing brush. They keep fence rows pretty clean too. The strip the bark off of trees, prune those low lying branches that whack you in the head when you walk past and do a pretty good job of keeping creek beds free of plant life but they’re kind of useless at keeping grass trimmed.
Do yourself a favor, buy a mower.

Courtesy of Danielle Langloism, Wikipedia CCL


One solution is just get synthetic turf installed for your goat pen. Of course you’ll still have ot feed them but you don’t have to worry about mowing the lawn!
You would, however, have to worry about them eating the synthetic turf so I wouldn’t recommend it.