When he was younger he raced speeder bikes, middle age he watched operas and appreciated art, so what did he do when he was emperor? I heard he liked to watch jedi kill each other in front of him. Anything else?
he found dark side holocrons and nexuses and increased his dark side powers; with no Jedi to stand in the way of his learning and searching anywhere in the galaxy he was able to increase his dark side power substantially
__________________ "Vader's pulse and breathing were machine-regulated, so they could not quicken; but something in his chest became more electric around his meetings with the Emperor; he could not say how. A feeling of fullness, of power, of dark and demon mastery -- of secret lusts, unrestrained passion, wild submission -- all these things were in Vader's heart as he neared his Emperor. These things and more."
An almost identical thread was posted on jedicouncilforums.net a few years back. Based on what we know of him, Palpatine probably attended operas, read books and holocrons on the dark side, possibly lightsaber sparred with droids, and played tons of dejarik.
I highly doubt Palpatine genuinely enjoyed the opera; I'm guessing the activity of going to the opera just formed a part of his fabricated public persona. A Sith Lord like Palpatine would be into something like thrash metal more likely.