To enter grand palace, just make sure you dont wear shorts or
berms. And take off all head gear. 
You may wanna go to the ruins at the ancient
city of Ayuttaya (or something like that) some distance from
bangkok itself. Plenty of local agencies to take you there and
pretty cheap for a day tour. There are other day tours also.
Otherwise go for a cruise down the River.
But!! But!! beware of over-friendly locals who hire tuk tuks for
you. Its a scam!
