The Octagon, built in 1322AD, from wood - and still standing.
I thought if asked this question I would choose something old from Europe until last month I went to Rio de Janerio and saw Catedral De Sao Sebastio. It is stunning. Only downside it was paid for by a petrol company. It's one of the few modern buildings that has made me catch my breathe. I wanted to stay for an hour or two just to watch the changing light.