I'm kind of surprised that Wat Pho (Temple of the Reclining Buddha) isn't specifically named in that link, it was certainly my stand-out sight of Bangkok.
It is on Rattanakosin Island though so I guess I have visited the area that may be proposed. I will admit I didn't realise it was actually an island until now, but have just noticed the canals on the non river side.
I don't know if you have been to Bangkok before Durian, but I have fond memories. I can't think of another city so well set up for independent travellers, especially if you have a limited budget (by Western Standards). You can make of the city what you like, but I enjoyed the couple of days I spent there.