I live in Rochester and have become friends with JP, who runs icheg. I got a tour of their collections and backrooms. Lots of really cool stuff.
They have a huge wall with computer magazines that go back past through the 80s. You'll be happy to know that every copy of Amiga World was there. I love that magazine.
One of the projects they're doing is to document every video game using video recording devices, so there will always be good quality demo videos of the games. I visited that room with him, and it was fairly large, with a bunch of shelves, filled with just about every console system you can think of, and just about every home computer as well... Including a boxed Amiga 1000. I've seen other Amiga artifacts there as well as in the "back room"... there's a cage wall that starts in that room, and about the size of a basketball court, or so, filled with racks and racks of shelves and drawers, filled with a ridiculous amount of games on CDs, floppies, cartridges for every console you can think of.
The place is overwhelming.
And yeah... everyone I've interacted with there has been really awesome.
(I've also donated a Kaypro II that I got from a friend that was in pristine shape, and I keep meaning to swing by to drop off my complete Amiga "Hitchhiker's Guide" box, and some Lucasarts boxes as well.)
All of this is above and beneath the main floor which has an arcade machine section, as you mention, but also essentially a huge playground area that teaches kids through play. My 4 year old loves the place, and actually is in their pre-school program.