For those of you who have previous experience of Bangkok, what would you suggest as the first thing to do/place to go for the first time visitor?

A river taxi... a good way to spend the first day as it allows you to get your bearings.... there are also some beautiful Wats enroute... You can get off an numerous stops enroute, finishing with the stop at Koh San Road.... Its really nice.

Get accomodations in the backpacker district and talk to the backpackers. Current informaiton is the most useful information.
Seeing the Royal Palace is a definate must do.
Splurge in an upscale restaurant, I believe we went to the Mango Tree and were extremel;y pleased. We have four children and two adults. A full course meal with pop, wine, and desert was around $40 US back in '99.
The night and redlight district is interesting as well if you are not turned off by that sort of stuff.
Walter
If you've been there, done that, you are fortunate
The majority of visitors head to The Grand Palace (and Wat Phra Kaew/The Temple of the Emerald Buddha) so maybe leave that for later when you've rested a bit. When arriving in a new place I like to go somewhere with a good view of the area. Jumping on a Chao Praya River Express boat is a good way to take in Bangkok for the first time. You get to see a lot of the cityscape and get riverside views of some of the landmarks. It's also very cheap. Consider going between the "Saphan Taksin" pier near Silom Road to the "Phra Attit" pier near Khao San Road (or vise versa). Another good first stop is the "Phu Khao Thong" (Golden Mount ) which is a hill with a large golden stupa and temple grounds located near the Banglamphu area, at the eastern end of the big Rachademnoen Road (the one with all the huge pictures of the King and Queen). You have nice city views from there and it is a relatively peaceful setting in the middle of the bustling city. Nearby is a canal boat station where you can get an interesting urban-style canal boat ride toward Siam Square and the Pratu Nam area. The "Baiyoke 2 Hotel is one of the tallest hotels in the world and there is a rooftop observation deck. There's a good map/satellite view of Bangkok here.

I agre with Captain Bob on what to do. I hope you do not stay on Ko San Road. It's full of stoned, dreadlocked farangs eating banana pancakes and getting tattoos. Stay ANYWHERE else.
Of the topic, but how do they get stoned? Ganja is not available in KSR as far I've seen (not that I do that anymore). Illegal drugs are so hard-targeted by police in Thailand in general you'd be a fool to try to buy/consume it in places like KSR. Maybe they're just "doped-up" on the heat and pollution(?)

Good advice from Captain Bob although you don't mention your interests.
Please be more specific about the things you'd find interesting and i'm sure some of us could point you in the right direction.