St Anne's Cathedral — the Church of Ireland Cathedral of Belfast — is a rather fine Romanesque building in the Cathedral Quarter that has been under construction since 1899. The spire, which was added in 2007, is made of stainless steel and rises 40 metres above the roof; it was called the Spire of Hope and it catches the light magnificently in the afternoon.
The interior is notable for its mosaic ceiling (a significant project undertaken over several decades), the baptistery, and the memorial to Lord Carson. The cathedral is also a venue for concerts and civic events, and it has a good café. It's worth entering regardless of your interest in religion — it's one of the better cathedral interiors in Ireland.