Hi Karen,
It is getting harder to find anything for under 2000 baht in a good location with a pool these days.
The closest I can get is Centrepoint Silom for 2600 per night. I think it's worth the extra, will include breakfast for 2, great pool, near the river and less than 5 minutes to the Saphan Taksin BTS station. They are renovating at the momment but it wont be a nuisance as it is happening floor by floor and you can expect prices to rise when they finish.

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I love Thailand this much