CT is a fine idea. Although, last year we went to Florence the day after Rome and the kids (14 and 10) loved it. The boy (14) liked the history and architecture, while the girl (10) liked shopping in the stalls with leather products.
On Day 1 we did the Road to Hana. Good choice. On Day 2 we did the sunrise at volcano. It was also a good choice, although we left the ship at around 3 am. We were back on the boat by 10am. There still might be time to go to the beach.
We are also from the DC area. Cheap and Honolulu do not go together (although there are inexpensive souvenirs in the Walmart). We stayed at the HIlton Beach Resort on one end of the cruise. Not cheap and crowded. On the other end we stayed at the Ala Moana. Nice place. If looking for "cheap" I would recommend looking at one of the booking sites and then read reviews. We flew from BWI with a change in Vegas. It was a lonnnnng trip each way.