Usually 见面 refers to seeing the person face to face. If you say "我想和你见面", it means that you want to meet that person face to face in general for example meeting a friend. "我想看到你" is used more often that "我想看你". Either way it means that you want to see that person really badly as if you reallly miss them or something.

In this condition 见面and 看 is changeable. But in other conditions it may be not. 看 is from single aspect. 我想看你去 means you are coming for him/her. 见面 is an action taking by both of aspects. 我想和你见面 means you and he/she are planing to meet somewhere. And like sjzh said, 我想看你 is weird if you are saying that you want to meet him/her.

I think there is little difference between “我想见你” and “我想和你见面”。 But “我想看你” is weird in daily speaking. It's not a natual saying.