Hi Brittany,
Whether you are staying at
Disney's Animal Kingdom Villas - Kidani Village or
Disney's Animal Kingdom Villas - Jambo House, you are staying at a lovely resort. Both of these resorts are beautiful in decor, and have exotic animals outside of nearly every window!
If you are using the complimentary Disney transportation, heading to each location that you mention from your resort will be by bus. You can take a bus from your resort to Magic Kingdom and Disney's Hollywood Studios. In order to get to Disney's Contemporary Resort, I suggest that you take the bus to Magic Kingdom. From there, it is a five to ten minute walk to Disney's Contemporary Resort, or you could hop on a monorail to get there as well.
My family often has our own car when we visit Walt Disney World. A benefit of staying at a Walt Disney World resort is that your parking at the Disney theme parks will be free. I have found that Walt Disney World has great signage, and I simply head out of my resort and follow the signs for where I am heading. If you have your own car with you, this would be my suggestion.
As for timing, one of the wonderful things about Disney's Animal Kingdom resorts is that they are relatively removed from other resorts and theme parks, which allows for expansive views and for lots of room for the animals to roam. This does mean that transportation to other parts of Walt Disney World can take a little while. Using Disney transportation, I would allow at least 50 minutes to get to Magic Kingdom and 40 minutes to get to Disney's Hollywood Studios. This should allow you enough time both to wait for a bus as well as travel time.
Please do let us know if you have any further questions, Brittany!