Quick post to highly recommend the two places we ate with our picky 3 year old:
Flatbread Pizza - GREAT location, GREAT atmosphere and really really good salads and pizza. I wish they would open one here in the Midwest. It is organic and local and close to the Ferry terminal, which means there is lots to do with cranky little ones while you wait for a table. Yum!
O'Naturals - again, GREAT location, Great atmosphere and I love their breakfast sandwiches. We had a flatbready kind of crust with egg, bacon, cheddar (just a sprinkle) and tomato. There is a nice place for the kids to play there - very safe and entertaining train table/dollhouse/books galore. It is just up the hill from all the great little shops in the Old Port area.
Sorry I can't give addresses, but in Portland, you go until you find it. What a great town.