Actually, the request is for a small group of 20-somethings who are going to be exploring that part of Spain this year in March, not walking. So they will not be in the albergue. I'm kind of their go-to person for advice, and I thought that some of the Vdlp folks might have stayed in a decent pension that would suit their budgets.
when I was in Zamora in the autumn there were some problems with the albergue having very restricted times which meant I couldn't access it. These have now been resolved, but I stayed in (I think) the Hostal la Reina just off the Plaza Major. It was cheap, basic, and run by a very caring French woman.
I stayed at Hostal Chiqui last fall. It is on the second floor at this address: Calle Benavente, 2
If you google it you'll have map of the city and its location. It's very near the Plaza Mayor (two minute walk). There are two other hostales in the same building, which together could accommodate your group of twenty at a good price.
Enjoy your visit at Zamora and make sure to go down the paseo down by the river under the walls, enjoying a few tapas with the famous local wine (Denominacion TORO) on your way back .