Hi, Karen,
There are lots of nice places to stop and spend some extra time-- Leon, Burgos, Santo Domingo, you will probably get lots of suggestions. I thought I'd just make a general comment or two. First, until you're out there and walking, you can't predict whether or when you will want to stop for either a rest day or a tourist day. I think many pilgrims are kind of surprised to find that a "day off" just feels funny. Not only that, you may find that the people you've become close to don't want to stop and if you do, you'll have to split up. I almost always take rest days, but I generally don't plan them -- I have an idea what the high point tourist places are on the Camino I'm walking, and then I work a couple extra days into my total but sometimes I don't use them, sometimes I take extras. It just depends. That's a long way of saying that I think the best plan is to leave things up in the air but allow for a few of these days off. Then if you don't take them, you can walk to Finisterre/Muxia or do something else from Santiago.
Private albergues will usually let you stay more than one night, the municipals will not, unless you have a medical need. But if you stop in the big tourist places, there will be a huge number of private choices in all price ranges.
buen camino to you! Laurie