Seems like a pretty broad spectrum: school to university to museums. What do you need the ideas for? If you can narrow it down you´ll get better answers…
Anyway, here´s a simple idea for a math game: The player get´s 5 cards with numbers and signs like “+3”, “5", “/2”, "(-1)” and why not include parenthesis cards. Then the player get´s two numbers: one is the starting number and one is the goal number. Then the player has to use his or her cards to reach the goal. It seems like a nice way to learn how basic math works and order of operations. You could also add a two player version where you can counter the other players cards, like putting parenthesis around two of his numbers, changing his plan.
If you want a game for a museum: spread out QR codes all around the museum and make an quiz app. Get the player to use the phone to answer some questions about stuff in the museum. “What is the period called when T-rex lived?”, and then you get A,B,C,D,E type answer. If you know the answer you can press A (or whatever the right answer is) or you can go to the T-rex in the museum and scan a QR code and watch a short info movie about T-rex. And you get the answer while you´re learning. You could use this for school classes like a competition: the group with most correct answers in shortest amount of time win.