Hey AD,
Depends how much detail you want to delve into, three full days activity easily, more if you delve into all the Wats and museums and like to just wander around places like China Town or the Weekend Market (Motto: "If it moves, cook it and eat it; if it doesn't move, peel it and eat it").
Best tip is the first thing to do is take the Skytrain (
http://www.thaifocus.com/bangkok/skytrainmap.htm) to Saphan Taksin and from there buy a 75 Baht day-ticket for the Chao Phraya Tourist Boat which also includes the waterbuses - it's an excellent way to orient yourself to most of the near-river tourist spots (whch is most of them). Take the Tourist Boat first and take in the tour commentry (in staccato 'Engrish') and then hop between the various piers by the waterbuses (normal and express: frequent, crowded) or tourist boat (less frequent, less crowded). This will get you around the major sites like the National Museum, the major Wats, Grand Palace, Barge museum (dull and charge extra for photos), China Town, Antiques Market. For Angkor Wat and Barge Museum alight opposite bank and take transfer ferry (included for BM, 5 Baht for AW). Nice little map and guide booklet included with ticket. AW best photographed from river in the early AM. Wish I'd discovered it earlier in my first tour to Krungthep.
Also the skytrain now reaches all the way to the weekend market (Mo Chit)