I really liked the Aachen cathedral. Architecturally, it was fascinating. The oldest part, sort of pre-Romanesque, was octagonal, the columns were heavy and there were hardly any windows (thank goodness for electric lighting!). The newer (well, 12th century) part is more what I'd consider high Gothic, with very narrow columns, lots of windows, everything reaching up toward heaven, very light. It's a great combination.
Historically, it was the first place I really felt that I understood a little bit about who Charlemagne was and how he thought. But also, how he fit into European history. I was inspired to hit the books to expand my limited knowledge. Definitely worth a visit!