We are official character meal addicts- it is THE BEST way to introduce a young or shy kid to the characters. It's amazing how much safety can be gleaned from that table between them and the character
So, having taken my daughter to just about every one since she was 2 herself- allow me to share our favorites. By far- number one- hands down for us is Tusker House (even better than Cind.Castle- which is saying something for a little girl). You get most of the 'fab five' in adorable safari outfits (and a picture with Donald before your go in). Goofy kissed my daughter on the head- and she still talks about it years later. And AK is an amazing park for little ones- there is so much for them to enjoy with the Safari and all the animal trails. There is even Triceratop Spin for the Dumbo ride experience. If you have your heart set on MK- there is no Mickey dining in park(although we enjoy Crystal Palace- Pooh & friends don't fulfill the need for the big Mouse). But for the nearby resorts: in addition to Chef Mickeys, there is also the Ohana breakfast at the Poly. It has Lilo and Stitch as well as Mickey and Pluto, who is a LOT of fun for toddlers. Plus- you can either hop a boat or the monorail to get back to MK, either of which will be big fun for a 2yo. Garden Grill at Epcot is really fun too- you can't miss with Chip & Dale and a restaurant that rotates, plus MrM and Pluto. Then you can ride Nemo and explore- but the downside is not many rides for the shorter set. We did Chef Mickey's for dinner, but were underwhelmed- the food was just boring compared to others (they all have mickey waffles- so it is only the adults who probably care about the food though)
I think those are the only four places where you will get Mickey himself, the other dining experiences are more 'girly' with princesses etc. I have always had good luck getting ADRs at 'non-traditional' times like around 2pm or 4pm for late lunch/early dinner. Of course- with a 2yo, your primary concern should be nap time. Wherever you end up eating, a well rested kid will enjoy it much better. I had mine fall asleep during a character meal once- and miss all the characters (although they did come back later to give her another chance)
And if worse comes to worse- I PROMISE you that at 2, the entire experience of Disney is going to be so amazing that you could give him carrot sticks in the stroller and it will be the best meal of his life