I like to get off the beaten path and go to small town America. I usually find that a little mom and pop cafe will have better food at a better price than tourist meccas. I ask the locals what their town's attractions are, and try some of those.
Just exploring the sights and beautiful places, and especially seeing how the local people live...one of my favourite memories of taking my son on holiday is when he tried to play football with a local boy, even though there were huge language barriers.
Based on the thread comments...holiday does not mean celebrations of a nationally recognized event but rather vacation...that said, I just like not to think about daily stuff like planning or technology or every day issues...
I agree that exploring the sights of beautiful places is a wonderful holiday activity. Some of those beautiful places have protection as national parks -- in many countries around the world. For a vicarious experience of family backpacking in one of America's lovely national parks, read the book UPS AND DOWNS AROUND RAINIER by Nancy Catton, ISBN: 0-7596-4658-9
If it's hot spend time on the beach playing beach tennis,swimming etc. Also like to see the "real" place and find a small bar and watch people. At night go for a couple of beers, then a restaurant, relax and chill out for a couple of hours.
Chess is pretty good. Easy to carry with you and gives your lazy holiday days a sense of achievement when you win. Also helps boring family holidays liven up with some healthy competitive spirit. Great brain exercise too.
I love exploring the local areas, whether this be on foot on bicycle. I think you get a true understanding for the local people if you know where they come from and what their surroundings are actually like.