You would have to go to TTL. The monorail only hits 2 parks, MK and Epcot. Do you have a rental car? I would suggest that. Nothing wrong with the busses or monorails, but it's just a lot easier to get around at your own pace to your destination.
What we did in June was walk from the Magic Kingdom to the Contemporary and took the bus from there to the Animal Kingdom. It is maybe a ten minute walk from the MK entrance to the CR. You will see the bus station for the CR as you approach the resort.
I just got back yesterday. I simply took a bus from MK to AK when the time came. I found that all of the parks had buses that would take you directly to another park without having to connect.
I don't believe that there are buses from the MK to any of the other parks. You must go to the TTC for buses to the AK and the Disney Studios.
Or walk or monorail over to one of the MK resorts to take a bus to the AK or the Studios.