Hey Cristi!
On the first day of our trip our family usually tries to do the Park that has the least amount of things we want to do that week. For us, that usually ends up being Animal Kingdom as we can clear that Park quickly. Or, we use that half day to do Downtown Disney and a great dinner.
It sounds like you will already be starting your vacation off right with dinner at Chef Mickey's! So, if Hollywood Studios has the least amount of attractions that you want to experience this trip and you feel like you can do it all before you have to get to your dinner, then go for it!
Another thing to think about is that Chef Mickey's being at Disney's Contemporary Resort you'll be right there on the Monorail. That could have an impact on your decision. One thought would be doing just one part of Epcot, like Future World, that day before hopping on the Monorail and going to dinner.
I hope you have a great vacation full of magic!