Someone already posted a link for electric mowers. Recently, I saw an ad on the 'net that was for an electric riding lawnmower, and it said it would mow 2 1/2 acres on a single charge, so you really don't need a gas mower if you don't want one.
That being said, it's really not that expensive to mow the lawn with gas. My fiancee lives on a large tract of land (her parents own a lot of land as well as a trailer park, all total probably around 4 to 5 acres of mowing) and it can be done for around 5 or 6 gallons of gas on a riding mower. (Yeah, riding mowers are the bomb, never used one until I started living here with her. Before that it was a push mower in the city.) We only have to do it around every 2 weeks or so.
As far as goats? Used to raise them when I was in high school, and they kept the grass golf course short and looking good. Also ate a lot of the weeds that would have needed a weed eater to get at. And, if you keep the doe away from the buck, the milk is actually better tasting (to me anyway) than cows milk, as it has smaller fat globs in it. Makes better ice cream too. Another benefit is that your skin won't break out like it does when you drink cows milk. Went through all of high school without any acne.
As far as the mow free May thing? Sorry, can't quite get behind that one as I like my yard to look good.