Is Taylor's Automatic Refresher too casual for what you want?
Delancy Street is open all day Sunday and has good food and would be an easy place to take babies.
In another direction, near Golden Gate Park, Park Chow always gets mentioned for good food and child friendliness.
Can you maybe give some restaurants you have liked, even if they are not in SF ... but bonus points if they are. It would help to narrow down what you think is excellent. Since this is your first post, please read the thread at the top of this board to help us help you.
There are a few thousand restaurants open on Sunday and many are child friendly. A neighborhood to shoot for would be nice too.
Another thought is plugging in the date and time on Open Table to see what it available. When I did that for Sunday at 2pm for four people it returned over 130 restaurants.