The Sagrada Familia was my first thought too. Definitely worth a visit! I think it very much carries on the spirit of Gothic cathedrals. Those builders used the best construction techniques of their time to create breathtaking buildings, and Gaudí did the same with the techniques of his time (and those who picked up the work after he died did the same). The interior with the tree-like branching columns is especially impressive...
In that vein, the Sagrada Família [1] might get finished this decade, was started in 1883, and is likely to be kept around for a couple centuries.
[1] https://de.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia