You can meet Spongebob at US in the Nickelodeon store where you exit the Jimmy Neutron ride. The times he will be there will be posted on your park map or show guide. I have never seen Dora there.
My son is a big Spongebob fanatic, too, and we've seen him many times near Production Central on the street where the Lucy store is. Poor guy needs serious bodyguards around 10yo boys!