Bangkok is a huge city, but most of the action is in the Banglamphu area, which is cheap and convenient to all the major attractions. I loved Khao San Road, the back packer's center- Where else can you get beer by the bucket? But beware as scams run rampant. If it's too good to be true- IT IS! You'll either love it or loath it, but worth at least a walk through for cheap souvenirs and people watching.
My highlight in Bangkok was a klong trip to a little temple that sells bread to boat passengers. Not Hungry? The catfish in the water beneath you are and boil the water trying to grab the free snacks as you drop them down. It was the closest I ever hope to get to being a celebrity with papparazzi around- the catfish are huge and agressive beyond words!
Quick Tips:
You will get your fill of temples and Buddhas on any tour, but if you go on your own to the Grand Palace complex, splurge on a licensed guide if you're a real history/culture buff. It's so amazingly detailed and intricate, you could walk right by important details in a euphoric daze. The massages at the temple school are a little more expensive, but highly rec'd after a couple hours of craning your neck to see all the chedis and buddhas.
Best Way To Get Around:
Try to stay off the tuk tuk 3 wheelers if time is an issue- they'll almost always run you through two or three stores hoping for a commission before you get to your destination- you didn't think 10 bhat would really get you across town did you?
Use the river service as your best friend; a lot of the major sites are on/near the river. They're as cheap as the buses, but don't face the nasty traffic snarls.
Everyone in Bangkok with a vehicle will be between you and your destination, so give TONS of time if you have to cross town to the airport/rail station, ect.