No museum is going to want the hardware especially if it isn't in perfect out from the box
new shape. Can you imagine how many people would be trying to sell or simply donate their family gaming console? Far too many I suppose.
Why don't you look around for a modern adapter and play the thing (if you have the cartridges/games to boot)? Or Ebay the thing for the cost of shipping the computer if you're not interested in keeping it.
I think the following link is perhaps the only brick and mortar video game museum presence:
International Center for the History of Electronic Games
In Rochester, New York.