Anonymous wrote:It'd be great if we could find a rental for less than $3,000 a week. If that's possible
OP, at this late date it's going to be a challenge. Things book up early for Christmas, and the Caribbean is very expensive then.
Try caymanvacations.com - you can search condos on Grand Cayman and the sister islands by desired arrival and departure date. I see that there is a 2 bedroom garden view in the Christopher Columbus condos on Seven Mile Beach that's available for around $3600. That's about as good as it's going to get, I think.
If you're interested in St. John, go to caribbeanvillas.com and again search by date. You'll notice that the Christmas / New Year's dates are incredibly expensive compared to the rest of the year. You may be able to find a small villa that works for you.
Grand Cayman is easier to get to than St. John - to get to St. John you have to fly in to St. Thomas and take a ferry. Also, you really need a car on St. John. I think you could do a week on Seven Mile Beach in Grand Cayman and be fine without a car. Note that you have to drive on the left side of the road in both locations.
I would expect flights to be at least $700 per person for either location.