Hi, Roger,
I got my key from the Museu de la Festa, which is a museum dedicated to the folklore of the area. So if you arrive during hours that it's open, that's the easiest, because the museum is right across the street from the albergue.
I know that the police also have keys to the albergue. I know this because when I was in the albergue, all alone and fast asleep, sometime after midnight, another pilgrim entered. He had gotten the keys from the police, who had told him no one else was in the albergue, so we were both a bit surprised, to say the least. I let out a half-asleep shriek of some sort, which scared him out of his wits. He was a Bulgarian cyclist whose bike had broken down numerous times on the way out of Valencia but he just kept on going till he got to Algemesí. So that´s a long way of saying that I am virtually certain you will be able to get the keys.
I don´t recall any private places in Algemesí, but the French guys I wound up walking with a few days later told me that they had gone 4 kms further on to the small city of Alzira, where there is a variety of accommodation, but no albergue.
I broke the Algemesí stage up with the first day only to Silla, then day two on to Algemesí. I always try to ease into this Camino routine, so that worked for me. I actually spent an extra night in Valencia, walked out to Silla, then took the train back to Valencia. I had the afternoon and evening to see more of that absolutely gorgeous city, then the next day took the train back to Silla and started on to Algemesí.
I was in a restaurant in the central square, and a big group ordered a paella, which I got to sample as well. Wow.
Beware -- the first four days have nothing but asphalt. It is murderous on the feet. But such a wonderful camino, so it´s worth it!
I will really enjoy hearing about your adventures on the Levante. Buen camino, Laurie