A few thoughts. I don't even know what brand it is, but we have one we bought from Wal-Mart several years ago. It's a thick plastic with an insulated layer around it. It's got a large shoulder strap, so you can easily carry it. I guess it carries about 1/2 gallon, so it's decent size. If you've got somewhere that you have access to a freezer, just fill it about 1/3 of the way with water and stick it in the freezer overnight. When it freezes into a solid block, it'll make it all day long and you can refill it several times. In fact, my family sometimes complains that it's too cold. We use it in the heat of June and July and it works great.
Also, if you don't want to carry stuff around, all the parks give out free cups of ice water. Just go to any counter service location or most of the kiosk type places and they'll give you as many cups of ice water as you want. Toward the end of our recent trip, we started leaving our water thermos at home and just doing this. Fresh ice water at any time, without having to tote it around. Fantastic idea.