That's pretty much the end game for now. You can do the dungeon and get the metal, power source and syringe. Metal is used when you want to train with him. which will raise your stats by a lot. Power source allows you to reset your traits you picked at the start of the game and pick new ones. And syringe raises your stats and mutates you. He also sells quite a few weapons you can't get anywhere else. You can give him the Ichor canisters you can find in the caves to get minor passive bonuses.
Viewing post in Bug reports
Pretty much. Now you can try unlock new outfits and cheats, get different endings and explore the rest of the map.
You can also try and fight Mr. White by talking to the purple guy who stands near the Riverstone Inn. You can fight him multiple times and he will be a little stronger each time.
You can raise relationship with him, but it doesn't really do anything right now, since he doesn't offer you any jobs and there are no events tied to it.