The museum itself is located on the second and third floors of the building. The building itself was once a Venetian arsenal but today it houses items from Mycenae, Tiryns, Dendra, Asine, Halieis, and of course a few from Nauplio. The museum is closed on Mondays. For some of the same reasons you are here though, others will be too, and sometimes it may get a little crowded. You may have to look around for a good deal on a room, but the first time I visited I was lucky and found an inexpensive room near the top of town which had a rooftop patio.
Kids play soccer on the courtyard while others sit on the museum steps.
There are a number of restaurants on the square also. The view is absolutely stunning and you can experience it to a small degree by following the link below where you can load a 360 degree view from the fortress. It may look impregnable, and indeed it was thought to be so. After all, it was designed by LaSalle in 1711, but in battle it fell after only an eight day siege. Its Kale, on the path just above the water's edge.