Hi Angela! Sounds like you're planning a fun trip!
All three of the restaurants you mentioned are close to the Magic Kingdom. Since you'll be inside the Magic Kingdom on the morning of 9/20 for your breakfast at Cinderella's Royal Table, I would definitely plan to take in the rides and attractions there before and after breakfast. If the park starts to get crowded by lunchtime, take the monorail over to Epcot, and plan to spend the afternoon there. If you're not worn out by the evening, you might want to catch Fantasmic at Hollywood Studios at 9 p.m. (It's scheduled to be shown on 9/19, 9/20 and 9/23.)
On 9/21, start your day at Animal Kingdom. It will be less crowded that day than the next one, as evening Extra Magic Hours are scheduled for 9/22. (Since you'll likely be having dinner at Whispering Canyon Cafe during those Extra Magic Hours, it would be best to avoid Animal Kingdom and the extra crowds that day.) To get to Chef Mickey's for your dinner reservations, take the Magic Kingdom bus from the park or from your resort, and then hop on the monorail to the Contemporary. The Magic Kingdom closes at 7 pm on this day, but you might have time to fit in a few rides before dinner. If you have extra energy after dinner, you could take the monorail to Epcot which is open until 9 p.m. and take in the Illuminations fireworks.
On 9/22, start your day at the Hollywood Studios. To get to dinner at the Whispering Canyon Cafe, take the bus from the park or the Pop to the Magic Kingdom, and then ride the boat to the Wilderness Lodge. The Magic Kingdom will be open until 8 pm on this day, so you could spend some time before or after dinner taking in a few more attractions.
Hope this helps! Thanks for asking me your question, and come visit me again if I can help! Hope you have a magical vacation!