We have enjoyed driving to Colorado and hiking in the mountains. Kids were 3 and a half and 3 months old (back pack worked great).
We had a fun vacation once in Las Vegas when the kids were 6 and 9. Great value on hotel and all the buffets are incredible. It was easy to walk or take the trolly. The airport seemed like it was only about 5 minutes from out hotel (Excalibur). We enjoyed seeing all the spectacular hotels and attractions, the fountains at the Bellagio, etc. We drove to the mountains and hiked one day, went to the desert one day, toured Hoover dam one day and did a helicopter tour of the Grand Canyon. We were hugely surprised that there was so much for a family to do.
South Dakota was another surprisingly enjoyable family vacation. We stopped at Wall Drug and the Corn Palace along the way from Illinois and both were kind of cool. We stayed near Keystone and enjoyed Mt. Rushmore, the Badlands and the Black Hills. Enjoyed it all. The kids were 9 and 11.
Our favorite spot for a 100% totally relaxing vacation is on the beach at St. George Island, Florida (on the panhandle). We rent a condo at 300 Ocean Mile right on the beach. Out one door is ocean and out the other door is the pool, no huge tourist trap stuff going on. A national park is right beside us at the end of the island. Biggest decisions to make are which level sunscreen to apply in the morning and where we go out for dinner each night. Appalachicola is nearby with some nice shops. It is a very family oriented spot, not a place where college kids hang out.
We have tried Panama City Beach (too crowded, too touristy), same thing with Pigeon Forge, Tennessee. We liked the hiking there, it's just too crowded.
We are hoping to visit Washington D.C. this summer, our kids will be 12 and 15.
Shorter trips that were fun; Door County and Wisconsin Dells in Wisconsin. At the Dells we stayed at the Kalahari Resort which has a huge water park. Had a blast.