The area which has seen the most consistent appearance of characters at both parks is right at the entrance after you enter the gates. It's just before you go down the hall of Main Street or World Bazaar.
The characters who have dedicated greeting spots are:
SEA: Ariel, Duffy & Shelly May, Mickey, Minnie, Goofy, Donald Duck
LAND: Toontown - Mickey, Minnie, Goofy, Donald, Daisy, Chip & Dale
There is no fixed schedule for any other characters, and face characters are particularly random. As mentioned previously, it really is best to ask a cast member, especially the ones standing near the Wait Times board. Otherwise your best chance is to wait around at the entrance area and see who comes. Or if you see a line forming against some sort of railing or to the side or in front of a door/gate, it's a good chance a character will come out.