Question: things to do after beating the elite 4?
Answer: Obtain 60 Pokemon and get the National Dex from Prfessor oak.
help Celio obtain Ruby and Sapphire. ... 
Go To Cerulean cave as Mewtwo is now obtainable.
you can catch one of the three legendary dogs(When you pick Bulbasaur, you can catch Entei. ... 
You can now challenge the Battle Tower.
Go on the Unown quest.