Hi Megan,
Thanks for coming back to visit us here at the Disney Parks Moms Panel with your question! It is a great idea to try and cut down on travel time by arranging your dining close to or in a Theme Park.
Both
'Ohana and Chef Mickey's are on the Monorail line so they are both very close to the Magic Kingdom. Once you are finished your meal, simply catch the Monorail and you will be whisked away to the front of Magic Kingdom. I actually find that after eating at
Chef Mickey's it is faster (but not as much fun) to walk to the Magic Kingdom. Simply head down to the front of the lobby and head toward the buses. The walking path will lead you around the parking lot and straight to the front gates of the Magic Kingdom.
Given that these two dining options are located on the Monorail, it is also very easy (and fast) to get to EPCOT. You will need to switch Monorails at the Transportation and Ticket Center, but it is another viable option.
To look further at the distances between dining locations and Theme Parks, take a look at the
Walt Disney World Resort Map.
I hope you have a magical vacation Megan. Please let me know if you have any other questions while planning. I would be happy to help!
Stephanie