Buses leave from Sanam Luang to all parts of the city, common choices include:
Ratchadamnoen Nai Rd: (eastern side of the park)
Regular buses: 2,3,6,9,15,19,30,32,3,39,44,47,59,60,64,70,80,82,91,153,201,203
A/C buses: 3,6,7,12,39,44,153
Na Phrathat Rd:(western side of the park)
Regular buses: 15,19,30,32,33,39,43,53,59,64,70,80,82,123,153
A/C buses: 3,6
The main piers in this area are:
Tha Maharaj for Thammasat University and National Museum.
The main piers in this area are:
Tha Tien for Grand palace, Wat Phra Kaew, Wat Pho
Watch out for dubious tuk tuks and taxis in this area - if you get in a parked vehicle you're asking to be ripped off - flag moving vehicles down.
To walk from from the northern end of Sanam Luang to the far side of Wat Pho takes about 30 minutes.