The highlight for me at Sintra was the Quinta da Regaleira. This is basically some rich bloke's country estate. I wasn't all that interested in the palace itself - really, once you've seen one stately home you've kinda seen them all - but the guy really went all out with the garden design. Got a lot of freemasonry-type bumf in there, with lots of little statues and grottos dotted around and a network of tunnels underneath everything.
The centrepiece is probably what's called the Initiation Well. This isn't a well in the sense of being a water source - though it is pretty damp down there - but is more of an inverted tower, being a deep pit with a spiral staircase around the outside, eventually leading into the aforementioned tunnels.
You read Naomi Novik's Scholomance trilogy? This is where they find the doors to the school in the third book. The queue to get down the well wasn't as long as the book implies; it was probably only a 15-minute wait or so.