We stayed in Hotel Abadia, which is about 3kms outside Burgos and near the University. It's spotlessly clean and it's right on the Camino. The staff were very helpful. It could be a nice little walk for you when you get off the bus, especially if you want to get your credential stamped and have a meal in the city. Or, if you arrive early in the day and want to go back to the city, there are regular buses.
However - it's a 'functional' place to stay, rather than a Camino experience. All in all, it worked fine for us as we spent the afternoon in Burgos, had a late lunch and picked up some basic provisions in a supermarket on our way to the hotel. We had fruit and yogurt in our room before leaving the next morning at around 6.30am. We were glad of the great sleep and the feeling that we had a 'head start' - especially since we were walking to Hontanas in intense heat.