I am taking a group of 7 in 3 weeks. I was fortunate enough to get reward tickets on Delta for all 7 of us. We will be renting a mini van, so as not to have 2 cars, (which I got through PriceLine for about $200 a week cheaper than the best deal I could find online) I have 2 or 3 BR condos rented for a week on Kauai and the Big Island. I have had good success with VRBO for condos in the past and going that way again.
If you are on a budget, that is WAY cheaper than 2 hotel rooms, by less than half. For only a week, I would second the recommendation staying on one island, you will spend a lot of time in transit, checking out, checking in, renting cars etc, you loose almost a full day. Also if you fly into and out of one island, you will save the cost of the interisland flights, which can really add up for 7 people unless you get in on the specials I got during the recent price way.
Cindi