It’s a few years since I’ve been so not completely up to date but as well as the Palace I’d recommend
– chatuchak market if you’re there at a weekend. Massive open air market selling earthing from handicrafts to endangered species. Worth half a day or more. Huge amount of street food there as well
– MBK shopping mall used to be the place for pirate software, fake watches, DVDs etc at much better prices than on the streets. A real experience in itself as well. Loads of other malls if you just want clothes or high end stuff
– try to take a canal bus somewhere. The canals are tucked away and take a it of finding but there’s nothing like the experience of a narrow boat powered by an un silenced , exposed, truck engine at the rear barrelling under bridges with inches to spare.