Sightseeing:
From wherever you end up staying, get up early and take the Skytrain to Saphan Taksin (change at Siam (pronounced See-aam) if necessary). Take the exit closest to the river and head for the dock (Central Pier) on the left with a booth. This is the office for Chao Phraya Tourist Boat - for 75THB you can get a day ticket for unlimited use on the express boat and taxis up and down the river. These boats stop at a number of piers along the river which give access to the R. Palace and Wat Phra Khaeo, Wat Pho, Chinatown and the National Museum on the East (Bangkok) bank. The cross-river ferry to the R. Barge Museum (beware extra cost for photography inside the museum on top of entry fee) is included but a similar trip across to Wat Arun will run you and extra 5 THB each way.
But the real attractions are the views of Bangkok from the express boat (with commentary in English, of sorts) and the experience of riding the stern of a packed river taxi - just don't expect to get a life jacket to yourself if anything goes wrong...
Also Chatuchak Weekend Market has to be seen to be beleived, again take the Skytrain to Mo Chit (end of the line) - you name it, they sell it.
Cheers,
K.