When I was a low budget student living in Utrecht, I furnished half my (admittedly small) apartment with things I picked in the streets during and after Queen's day.
The best street markets are those away from the central and most touristy part of the Dutch towns and I personally didn't like Amsterdam on Queen's Day: it looks too much like the night before, only that all the side effects are visible under the sun.
The "balcony scene" of the Coronation, with the new King and his wife waving their royal hands to the crowd, is at 10.30 on the Dam.
For those really keen on seeing the Coronation in style, but unwilling to go to Amsterdam, the cinema Pathe Buitenhof in Den Haag will show it live on its screens.
Happy Last Koninginnedag!