I wish I would visit the statue of liberty [closed]

The quick answer to your question is yes, you can use that structure. That's because there is an implied that between the two clauses: "I wish (that) I would ..."

But a better and more important question is whether would is the best word to use in this sentence. Most English speakers would say "I wish I could" here, meaning either "I wish I had the opportunity" or "I wish I had the ability..." Writing "I wish I would" is uncommon. It implies that you're not doing something because you lack willpower or volition (and even in that meaning, many English speakers would still say "I wish I could..."). For example, you might say, "I wish I would stop eating candy bars right before lunch."

Theoretically, you use I wish ... would .... When you want another person to stop doing something or you want them to do something

I wish she would stop lying. I wish he would be nicer.

You want things to be different. But in your sentence, there is nothing you want to be different. You just wish to visit a place ... I hope it helps.