Hey there, Tammy!
You could not be in a more perfect transportation position. You have a couple of great options to get from your fun day at the
Magic Kingdom theme park to a fabulous meal at
Chef Mickey's restaurant, and they are pretty easy peasy.
Chef Mickey's is located in the A-frame building of
Disney's Contemporary Resort, which is conveniently located right next door to the Magic Kingdom. The easiest way to get to the resort is via a walking path. When you come out of the Magic Kingdom, you'll head left down the path toward the Contemporary. It's about a 10 minute walk, although if you have little ones walking with you, I'd allow 20. My girls always wanted to chase the lizards or look at a flower, so the walk was definitely at their leisurely pace.
You could also hop on
Disney's Monorail Transportation. There are monorail stops at both the Magic Kingdom and the Contemporary resort. I always say you should allow yourself a little longer to take the monorail - say 30 minutes. You will have to wait for the monorail to come, and you want to factor in some time to make other stops.
Wishing you an absolutely magical time on your upcoming visit!
Anna