Wailking is the best option to visit the main attractions of the city, but there are some places of interest you can take public transportation or rent a bike to get there.
By bike
Bicycle is a good option for visiting all atractions of the city. Burgos has a very good bicycle lane that connects several points of the town. Also there is a public rent service for bikes called bicibur (http://www.bicibur.es/). Riding a bicycle in Burgos is a good activity, there are no big slopes and riding along the rivers or in Fuentes Blancas are very interesting activities.
By taxi
Official taxis are white, and have a reddish stripe on the front door. The tariff is displayed on top of the car a 1 during daytime, a 2 during the night, which become 2 and 3 on holidays such as Christmas Eve. You can take taxis in the taxi ranks all around the city (http://www.aytoburgos.es/...), also you can call in advance +34 947 277777 or +34 947 481010.
By car
Transportation by private car in Burgos is not difficult. Altough looking for a place to park in the city center can be very time consuming unless you park in private parkings.
By bus
Burgos has an extensive system of city buses (http://www.aytoburgos.es/...), which you can ride for just 85 cents. You can buy the ticket on board.