Now we have some info.
The most expensive Hyatt ?. I suspect those who are Hyatt regulars have stayed in many expensive Hyatts. I doubt anyone has ever went to the trouble to find out which one is the most expensive, so likely the best you can get here is a guess. You also have seasonal factors. The most expensive in Summer might be way down the list in Winter and vis-versa. If you take a couple dates (regionally adjusted) and then go to the Hyatt site and start the booking procedure to see the price, then you will know. Starting with the Hyatt reservation line would probably narrow this down to a couple as they would be the most knowledgable.
Question 2, we now know, is where each of us has chosen to use our NAN. I will be staying at the Hyatt Regency Hill Country Resort. We actually extended our stay a few extra nights with points. It will be our first stay there. I researched on the web all the activities we like to do that are in the area. Based on the logistics and time frame guesses, I was then able to establish the number of days for a rental car, where to rent it, the number of nights a the hotel, etc.
Five nights (sometimes many more) in one place is no problem for us. If one knows his likes and dislikes and is willing to spend the research time on the web it is easy to come up with day trips from a central point (HYatt) that will be enjoyable. In Australia, we have spent 8 nights (5 + 3) in Sydney in two trips. We have exausted Sydney for our purposes. We have spent 3 nights at Sancuary Cove and easily exhausted our interest there. We have spent 9 nights in Perth and will need another 7 to finish that area. We spent 5 nights in Melbourne and could use 2 more. We spent 5 nights in Adelaide (about right for us). All these stays were at Hyatts.
I also understand the not wanting to spend 5 nights in the same place. We have many friend that have this issue. We spent 5 nights in Auckland (enough) then 8 more nights in on the North Island of New Zealand with 2-2night stays and 4-1 night stays. We drove all around the island and some inland. Each place we stayed had a meaning in timing and sightseeing.
In the South Pacific, we will cruise next year. No one place had any real sightseeing opportunities for us. Snorkel, sun and fish are not on our list of activities. Each island will like offer a tour that we can enjoy.
I believe one could stay five nights at the Kauai Hyatt and have no problem having a good time with or without leaving the resort (we have been there twice for extended times and still have not spent more than a full day at this beautiful hotel). I also believe one could stay 5 nights at the Hyatt Scottsdale (in season) without really venturing out (we have about 18 nights of vacation with a few day at the hotel without venturing out).
Remember you do not have to stay 5 nights (gulp, what a waste) if you do not or cannot be in one place that long. Let the reservationist know you have 5 nights but only want to stay X and they will do that too.