I you want to stay in the historical center, the Hotel Isabel should be your choice. During your stay you will feel great thanks to the excellent cleanliness of the rooms. They are very friendly and they have an efficient WiFi network, one of the best in Spain.
If you want to enjoy your stay with your family and friends, you can do it in the Hotel El Valles, that is specialized in weddings and events. It’s an option to sleep in Briviesca, even if it’s located next to the highway and the restaurant is ordinary.
Finally, if you are not looking for a hotel, you should stay in the Hostal La Vid, a very recommendable hostel. One of the strengths is the human factor, there you will feel like at home. Clean and comfortable, don’t miss the free buffet breakfast.