Albergue Yesus y Maria on Calle Compañía and you will find it if you follow the flechas amarillas into the old parts of the city. You will see the signs. The albergue is not so far from the Cathedral. I liked Yesus y Maria a year ago in May, you can wash your clothes and get them dry, they had a coffee automat for the breakfast coffee, you can recharge your cell phones, ipods and cameras by your bunk, no problem. I visited the Cathedral for the pilgrim´s blessings in the evening. Yesus y Maria opens at 1 pm and fills up quickly.
But there are also other albergues in Pamplona, like Albergue Casa Paterborn operated by a German confraternity.
And youth hostels and hotels.
more info here: el-camino-frances/topic6856.html#p40332
In this photo you can maybe see the backpacks on the left in the queue by the albergue street door and the pilgrims to the right in the shadow. It was hot 32° celcius.