It is very busy on the islands in the first week of July. There are parts of all the islands that there will be traffic due to the lack of roads and hyw on most of the islands. However if you book a rental car in advance you should be able to get one and the traffic will not make it hard to get to your destinations, all though it could be a little annoying.
Excursions on the Na pali are fun but will be repetitive since the ship also brings you around the Na pali coast as you leave port and you will get to see the amazing beauty from the deck. I know that Makana charters and na pali explorer are Hawaiian run companies and have a little more to offer than some of the others.
On Kauai I had a lot of success booking excursions through a company called Kauai Discount Activities. They made my short stay on Kauai so memorable. They were a lot cheaper than the cruise and had a great selection of tours. If you take the free Aloha Center Shuttle from the harbor, Kauai Discount Activities is located inside of the Aloha Center. Their contact information is: 808 245 1770 or firstname.lastname@example.org. Call in advance because in July activities do book up!
We had a great air tour which took us across the whole island, na pali, Waimea canyon, waterfalls, mountains and beaches, we saw it all and was the high light of our trip!