I would suggest if you are going to do a sunset proposal over dinner to talk with the Hyatt concierge. They have a beautiful setup for a sunset dinner on the beach- very romantic. Definitely propose the second night if you get in really late the first day. You don't want to be tired and jetlagged. You may also want to consider a sunset dinner cruise, but it wouldn't be quite as private. My husband proposed to me on a beach (it was the 4th of July so we even had fireworks!) On the beach is really the way to go, I think. (Don't even think about popping the question on the plane or in the airport - yuck. She's going to want to be in a pretty dress- not tired and grungy from a long flight!)
All the best!
I think it should be done the first day you get there. This way she can show it off the whole week and your week will be soooooo awesome and you won't be stressed thinking about it or hiding the ring! It should definately be on the beach because that is so romantic. I love the idea of the sunset service at the Hyatt but even if you just do it when the sun is setting and you guys are just hanging out walking down the beach thats cool too! My friend was at the Newport mansions and her husband asked her to take a picture of one of the mansions and when she turned back around to look at him, he was on his knee and she was soooo surprised. Girls arent too picky when it comes to diamonds and sunsets! The idea on the plane is cool too but then you have to sit all excited the whole way there and she'll want to call people and she won't be able to cause shes on the plane. Beach= Romantic!!!!