Educational versions of musical chairs can go on as long as you'd like, especially if you remove the opportunity for missing a chair and getting "out." Simply have the number of chairs equal the number of players, and everyone will get a chance to sit when the music stops.
Different versions can include finding matching colors, shapes, numbers or words and any variation thereof. Simply make badges, necklaces or cards for each child, and have each badge represent a symbol that the child must find attached to a chair. For example, when playing with shapes you could have triangles, rectangles and circles (or more depending on the number of players) and have matching shapes with matching colors on the chairs. The children will have to find the chairs that match their cards or badges before the music ends. The amount of possible variations means that this game could last for a very long time, as long as the children remain interested and have fun.
In these longer variations of hide and seek, the children are not the ones doing the hiding. Instead you have two options. Either you can hide items around the room (cards with images, small toys, etc.) or you can ask the children to find already existing items in the room of a certain color, shape, size or type. One example would be to gather the children and allow them one by one to find items in the room that you specify; for instance, you could tell a child to find a red item and bring it to the front. This allows children to learn colors, shapes and other details and gives them a sense of accomplishment when they complete the task.
You can set up areas called centers around the room, and have each center be devoted to a particular type of learning activity. One center can contain easy-to-use art supplies like crayons, washable markers, colored pencils and paper; another can house books; and yet another can have educational action figures or toys that represent animals, characters from myths or dinosaurs. Free play in centers allows children time to freely explore and cooperate with one another and you as the adult can be available to facilitate play or answer questions.
Fill a bag or pillowcase with several common household objects. You can include stuffed animals, a set of keys (toy keys may be more appropriate for this game), cups, a book, or anything else you think would spark the imaginations of children. Remove each item from the bag, one at a time, and encourage the children to create a story by making one sentence for each item. The story will end when the last item is removed from the bag, but there are no limitations around how many items you can include or how many times the game can be played to change the stories.