Hmmm... Well, the Elite Four is the end of the normal story, but there's still some stuff left to do. There's a post story revolving around the Sevii Islands, though. Remember when you had the option to go to One Island after beating Cinnabar Gym? I believe you can go to Vermillion and now ride the boat to the Sevii Islands. There's a bunch of stuff to do there.
Aside from that, there's always completing (or trying to) your Dex, as well as catching Mewtwo in Cerulean Cave (which should now be open to you; go up the Nugget Bridge above Cerulean, surf down the water, and you'll find a cave).