I just wonder
To be sure. Earlyer in japanese anime or video games: main character lives in 303, important thing in some games is in rom 303, if someone in anime gets in the hospital (main char.). Its room 303. Mabye it's just coincidence. Does it have any symbolic meaning in Japan?

Question

Answer

Well, I don't think so.
There is no symbolic meaning for 303 in Japanese culture as far as I know.

As a room number, 303 is very common number because it means the 3rd room of the 3rd floor.