Where did Chuck Noland go in the end?

My guess is he decided to follow the girl and tell her about the package he left on her doorstep in person.

Judging by everything that had happened in the film and his expression at the end, I think he castrated himself and then traveled to Tibet to become a Buddhist eunuch monk. But then the temple bells inspired him to create a new form of rock music, so he returned to the U.S. where he became a huge pop star. But after ten years that got boring, so he earned a doctorate degree in nuclear physics and invented the world's first clean fusion reactor. But one year after that, the alien grays, astounded by his genius, abducted him into their UFO and conducted experiments on him for two years. Afterwards, they traveled back in time to the moment when he was at the crossroads and left him there, restored to the same condition he had been in originally at that time. Then, he went back to settle on the ranch and eventually married the woman. But that's just my opinion.

OR, maybe some semi ran him over while he was standing in the middle of the road. This occurs right after the picture fades to black and the credits start rolling.

It’s still not entirely definitive, but right before the screen fades away to black, he looks down the road that Bettina drove down and he gets this little smirk of a smile right before it goes black so I’m kind of thinking he went back to her house.

I mean after all, and I just figured this out literally yesterday but since the movie is not called castaway; it’s called Cast… Away, as meaning something was being cast away, throw it in the trash, whatever. Chuck was cast away and so was Bettina by her husband.

James Lipton asked Tom this same question. Iirc, Tom said "he went back and made babies with that woman".

On Inside the Actors Studio (Inside the Actors Studio: Tom Hanks: 2 (2006)), Tom Hanks was asked by James Lipton what he thought happened to Chuck after the film's ending. Hanks responded "He turned around. He went back and made babies with that lady".

He went and doggies the sculpture lady

I believe he thought about that spicy redhead getting out of the truck and decided to go down there and tell her that was the (now) famous Chuck Noland that survived a plane crash as well as being on a deserted island in the middle of nowhere for 4 years. I mean, do the math: the story starts off where Bettina is sending her husband Dick a package in Russia where he's plowing Yelena's patch. When Chuck is there at the END of the film, you see Dick's name removed so perhaps Bettina decided to swear off men for a bit...

Either way, it would make for a hell of a story to go to her place, and tell her in person that "this package saved my life". Even if she thought it was a bit odd, perhaps she said, "well then, let's grab a beer, cowboy". I mean, her smile... lord have mercy that woman was beautiful. May she rest in peace IRL.