The proper question you would like to ask, based on the Spanish question, is "Which countries would you most like to travel to?". It asks preference amongst all the countries one may desire to travel to. The other replies to your question seem to miss the point of the question. Those questions ask something like "a cuales paises quieres viajar otra vez para ver mas?". My question asks something like "a cuales paises deseas viajar mas que todos los otros"

I think you answered your own question: "Which countries would you like to see first?" alternately: "Which countries would you most like to see?"

it is nearly correct.. You can say which countries would you like to travel more to and explore? Or which countries would you like to see more of?

"Which countries would you like to explore more?"