Famous sites within walking distance from Khao San Road include the Grand Palace with Wat Phra Kaew, Wat Pho, Wat Arun, Sanam Luang, Wat Ratchanaddaram and the Golden Mount. See Rattanakosin for details. There are also some more adventurous options:
If you're up for a fun walk, hike to the Royal Barges National Museum at the other side of the river in Thonburi. The walking tour goes over the Pinklao Bridge, through a typical folk neighbourhood follow the signs and ends with the sublime royal barges.
Only on weekends, the Taling Chan Floating Market in Thonburi can be reached by bus 79 from Ratchadamnoen Klang Road. Ask a local where to get off, or you might get lost.