DD was very picky at age 2 and 3. You might want to consider using Garden Grocer and having some of her favorite things delivered to your room upon arrival. That is what we have done on our trips when she was those ages. We ordered her usual favorites in fresh fruits, fruit cups, raisins, cereals, snacks, juice, along with bottled water for all of us for the room and parks etc. Since she is not a morning person, other than a Tusker House breakfast on AK day, we would do breakfast in the room with her eating her usuals and DH getting resort CS for us. That way we also had things in the room that she could snack on when we got back at night if she had turned her nose up at dinner. We took little boxes of raisins into the parks with us for snacks while standing in line, or in case she refused to eat her meals.
As far as restaurants, for some reason Biergarten has always been a huge hit with her. That kid eats more there than anywhere else. Crystal Palace was another one where we found several things she liked. At 2, the buffets are also a great option because she will be free for buffets until she is 3. Other restaurants, you will have to pay for her meal (or let her eat off your plate...which there was no way I was going to order and limit MY food around what picky DD might want to eat; plus she was independent and wanted her own meal; and she was in the over 95% of height and weight at age 2, and if I ordered a meal that she turned out to love, there was not going to be enough for both of us!). We found that she ate better at lunch because in the evenings she would be a little tired.
Just a warning, if yours is a chicken nugget kid, mine had never met a chicken nugget she did not like until she got the ones from the kid's menu at WDW. She completely turned her nose up at them and we tried them in more than one place. I tasted them and I have to agree they were pretty nasty.
It would really help if you would give us an idea of what your child will eat. We had a real problem finding things DD would eat at most WDW CS, because she was not much of a "kid food" eater other than her beloved chicken nuggets. She would not eat the WDW chicken nuggets because they were nasty; hated hamburgers and hot dogs; would not eat mac and cheese; hated the disney peanut butter and jelly things that came in a bag; Disney only has Pepperoni and cheese pizza and she only ate sausage pizza at that age, etc. We had much better luck at the buffets and at TS. Tony's, Mama Melrose, Chef's de France, were big hits menu wise because they had pasta dishes. Akershus was another big hit because they had grilled chicken.