Baugher's farm has a nice little pasture with a miniature cow, a sheep, two alpacas, two donkeys and a bunch of goats. You're allowed to go directly into the pasture so you can literally just sit down and lounge with them and feed them treats. The alpacas are particularly friendly.

The the Zoo's barnyard and Elioak as mentioned above are both wonderful and my 4 year old has a great time there. They both have goat corrals where you can hang out with goats and brush them. The other animals are fenced off although the emu at Elioak is really friendly and will come say hi. Also the giraffe house at the zoo allows you to get very close to the giraffes if you go during feeding time.