The next morning we headed to Chao Phraya River (one the most popular attractions in Bangkok) by sky train (Saphan Taksin station). You can buy One Day Unlimited rides for sky train (highly recommended price B120 per person).
Meanwhile for Chao Phraya River cruise, there's also One Day Unlimited Tourist Boat (price B150 person, buy 2 B250). There are 13 piers that you can stop and each one has their own attraction.
We stopped at the Maharaj Pier which brought us to The Grand Palace and Wat Phra Kaeo. Admission is not free (B25o per person). We found its quite interesting and suddenly things became familiar... Oh yeah this is where Anna and The King was filmed.
After a few hours, we took a boat ride until the last pier and turn back to our first pier (Sathron Pier) and headed to town. Since we bought unlimited rides for our sky train we were able to stop at most of the stations. Most of them are linked to the shopping mall, which I think is a good idea. Siam Paragon, Siam Square, Central World, MBK, Siam Discovery are few that I could remember. There are a lot more that we didn't go.