Bangkok, like any capital city has a lot to offer. One being the Grand palace which is a must to visit and the nearby Watpo. The temple of the Emerald buddha is amazing and is one of the most religious sites in Thailand -the temples in both Wat Po and Grand Palace are stunning.
Dusit Zoo and vimnaneck Palace are situated in an area that is more European than downtown with tree-lined roads and the big zoo - 50bt nice to walk around and breathe!
Vinmaneck palace and grounds is massive and the Vinmaneck mansion has collections from around the world.
A boat trip down the river chao praya is worth it for the view of Wat Arun that is decorated with Chinese ceramics, also nice at sunset on the river.
Walking around Chinatown, just near the main station is nice for wandering around little back alleyways of markets and stumbling across Chinese temples - it's like walking into HK.
Finally thai boxing is a must when in the capital, stand at the back where all the insanse amounts of money are bet on the fight, really good atmosphere and well worth 200bt.
Quick Tips:
When in Bangkok don't fall for the 10bt tuktuk scam where they will say they will take you to seven places - sounds good but they will also take you to a tailors and jewlers - some who can be nasty - metered taxi is better but not quicker.
With Thai boxing make sure you go straight to the box office. People outside will persuade you that the back is full and they only have ringside. Ignore them!
When bargaining at market stalls always offer 1/2 and work up - they make a really big profit so can afford to go low.
If you go to the Grand Palace make sure you wear long trousers and covered feet or they will make you wear clothes that look like 70s flares!!
Best Way To Get Around:
Don't bother walking round Bangkok just for the sheer size and smell of Bangkok. The most comfortable way is by metered taxi w/ aircon but make sure they put the meter on.
Tuktuks are a good laugh and are more nippier than the taxi but if you get a bus the smell is horrible! To get from the main train station to Ko Shan you shouldn't pay more than 70bt for a tuktuk.
Local busses are by far the cheapest way of getting round however it can be very stuffy and if you get in a traffic jam it could take you ages.
If in Siam Square area the best way is the BTS skytrain, very efficient, w/ aircon and relatively cheap.