The best way to get there, I think, is the boat to Corfu Town - trip available from San Stefano Travel. Bus to near Kassiopi, then a nice boat ride with Captain Aris, who is a bit of a character! Great views of the east coast, and probably a little trip down to the end of the airport runway, where, with luck, you'll see a 737 going over you at 100 feet.
The boat berths in the Old Harbour. Walk up to the road and turn left past the Corfu Palace Hotel and the museum is about 20 yards up a little side street. It's clearly marked on most maps of Corfu Town. Allow at least 1.5 hours is you want to read all the great diagrammatic displays, and longer if you want to watch the videos, of which there are many.
You'll probably want a snack before the return boat trip. Coming out of the museum, turn right up the hill, and just across the junction there's a sports bar probably equipped with locals drinking coffee. They do a very acceptable toastie washed down with a cold beer.
Having suffered Corfu Town in summer temperatures, which can be a bit like trying to walk in a giant microwave, I found this trip with the cool museum very enjoyable.
You get to jump off the boat for a swim on the way back, if you feel so inclined.
The museum cost 7 euros for grownups and 3 for kids and old farts. Currently, it's closed on Wednesdays. I hope plenty of people will go. The staff there were extremely proud of their new museum. BTW, they have free lockers for your bags.