The quick answer would be the beginning.

Present your gift once you settle in your host's home and when you are greeting everyone. They will most likely open it immediately or ask if it is okay to open and you can just say yes. It will be a good conversation starter.

You might have probably read in a few places about various very traditional Japanese manners of gift giving but basically there are no strict rules when it comes to casual occasions.

So instead of thinking it in terms of etiquette we would recommend thinking of the gift giving gesture as more of a way to help everyone relax a bit more for the Nagomi Visit.