the idea of busing or train-ing off camino for a break is wonderful. there are plenty of interesting places to see or relax.
I think all bigger cities on camino merit an extra day or two (for sightseeing or just soaking up the atmosphere): pamplona, estella, logrono, najera, santo domingo, burgos, carrion, sahagun, mansilla, leon, astorga, ponferrada, melide, santiago. I really cannot say which is my favourite because each has its own charm. there are easy excursions from them, as well, some can be done on foot if you are inclined to walk a bit.
I think that in general private albergues would be more inclined to let you stay an extra night then municipal and parish ones, but that would also depend on the number of pilgrims expected to arrive and the number of albergues in town. I stayed an extra day in parish albergue in burgos (which is off centre and apparently not yet well known so it had space), municipal in mansilla (because I was sick, they even accommodated six sick pilgrims that extra day), municipal albergue in leon (where I got my own room for 13E so I could sleep off to my heart's content).
you could plan so that you sleep as close as possible to a big city, walk for an hour or so the next day, sleep overnight, and perhaps also take the next half of the day off, before heading to the next closest albergue.
in most big cities there are also youth hostels (albergues juveniles) which don't have one night policy: pamplona (on outskirts, and backpacker's in centre), estella, granon (1km off camino), burgos (on outskirts), carrion, leon (two in centre during summer).
if not, there is usually a hostal/pension which is affordable (about 25-35E for a single a night).