Disneyworld
We went to Orlando in 2008 with 3 kids aged 11, 8 and 3 - for 2 weeks. We decided to go to Disney parks only, and we had a wonderful holiday!
I did do a lot of planning beforehand, from Guidebooks, websites and friends - and it paid off. We bought our tickets in advance from an American site ( can't remember which one). We bought 7 day tickets, with the Water parks add on, and without park hopper. This meant we could have 7 days in the theme parks and 7 visits to Disney water parks. We went to Magic Kingdom 3 times, Hollywood Studios twice, and once each to Epcot and Animal Kingdom. Our favourite was Hollywood Studios.
We only took one day off from the parks - but we did pace ourselves. On most of our theme park days, we arrived at opening time, and stayed for an hour or two after lunch. So we had a relaxed evening at our villa, a swim etc. On one theme park day, we arrived late afternoon, so we could see the night time parade after dinner in the park. On 5 different days, we visited water parks. We arrived 2 or 3 hours before closing, when it was starting to quieten down, and it was relaxing.
So even though we didn't have complete rest days, we had plenty of 'down time' every day, and we made sure we had a relaxed meal, in air conditioned restaurants, on each of our park days.
It is worth doing some planning in advance. Do you want to get to night time parades or fireworks? You'll need to check which days they are on.