I currently have 5 goats and we are on a little less than an acre. My two Ober milkers are in the front yard and have a nice bed/food area on the patio. My Ober doeling, Nigerian mama, and Nigerian doeling are in a different area with a little house that the previous owners used as a play house. Everyone has plenty to eat and lots of room to play...I'm in the Oregon forest so there are lots of wild things to munch.
The great thing about having them where we have them is that they are very close to the house. The two milkers can walk right up to the sliding glass doors and windows and see us, which they love. They are a part of our family. The little goats are slightly more isolated, but their pen shares a door with my milking room, so they can come in to eat their grain and socialize. Plus we spend a lot of time with them.
Also I took one of my Obers in to the vet yesterday (she got stung by a wasp, we think) and had a fecal done just because I was curious. Her worm count was zero. Nada. And I have never wormed her, except with the herbal stuff. The vet said that this is what happens when goats are kept on browse and hay instead of pasture. Pasture is for sheep.
The breeder that sold me my Obers has been doing this since the 60's and is very well known out here. She swears that the best way to "do goats" is to have them dry lotted. (Is that a word?) Her girls (at least ten, last time I was out there) are kept mostly in the barn, and their yard is considerably smaller than either of mine. Yet they are all beautiful, award-winning, incredibly healthy Oberhaslis.
So to sum up (if you read this far) I don't think you need a lot of room AT ALL to keep goats. The only thing to remember is that you will need to buy a lot of hay. A lot.