All three of the "newer" buildings have 2nd floor balconies. These are Tokelau, Tahiti and Rapa Nui. All 1st floor rooms have patios; some of the patios are "blocked in" by mature foliage (tropical shrubs), while others have open access to grassy areas. Most longhouses have mostly grassy areas, with the exception of Tuvalu, which has mostly shrubs, and Fiji, which is probably about 50/50. The patio itself is the same in every longhouse, but it can feel bigger if you have grassy area, or more private, if you have shrubs. If you want a slightly bigger room with either a patio or balcony, request one of the newer longhouses. We have requested "either a balcony or a patio" a few times and our request has been granted.
I would call back and have it noted on the original reservation. From what I understand, they try to accommodate requests that are on reservations, but they ignore faxes that are sent later.