"Seems to be the main college you have to see?"

There isn't one in Oxford. King's Cambridge - at least its chapel - is just sublime: there isn't a college building of that status in Oxford.

Christ Church (just Christ Church: again you're confusing cities: Christ's College is in Cambridge) is the college that gets most visitors. It's big enough to absorb big parties without seriously disturbing the residents (a real concern), it's got the alleged Harry Potter connection (not to mention the undoubted Alice connection) and the quirk of having the local cathedral (and focus of pre-Reformation pilgrimages to the city) as its chapel. It's architecturally bleh, though.

The city's icon (and King's Chapel equivalent)is Radcliffe Square, its Camera and associated non-collegiate buildings and the view from the square into Hawksmoor's North Quad of All Souls College.