We took the train to Solvang from the LA area and it was a great trip. Even the bus ride from Santa Barbara was good which was part of the Amtrak ticket.
We were able to see many little coastal towns on the train ride to Santa Barbara and the view out of the Surfliner was great.
I do recommend that you get a business class ticket as this will provide a free snack and drinks on the train and a nice seat with a great view. The drinks and snacks on the train are expensive.
Check out the AMTRAK site for more info on getting to Solvang by train.