This will probably ignite a nasty debate, but something needs to clear the cobwebs out of the forums anyway!
It took me 4 visits to actually appreciate Bangkok....the first 3 trips I thought of it as the armpit of Asia - dirty, polluted, obnoxious, I couldn't wait to get out of there fast enough. The last trip there was really only made enjoyable by some people I met and the partying that we did. Now, like many others, I am a convert and actually find myself craving
the madness. Aside from the shopping and partying, there aren't many good reasons to stay there.
My advice, if I had less than a month to spend in Thailand, I would get out of there as fast as I could book a train or bus....there are many more beautiful and charming places waiting to be explored outside of the city. That is just my opinion.
Oh yeah....I would save the islands for last...seriously, because once you get into the Andaman it is damn hard to leave...you'll find yourself sacrificing Chiang Mai days if you go there first.