Cologne

There are 2,000 years of history in Cologne, and visitors here will find everything from Roman towers to Gothic churches to fine examples of modern architecture. Cologne has a variety of museums, too—check out the Museum of Applied Art, the Museum Ludwig and, if you have a sweet tooth, the Chocolate Museum. Be forewarned, though—the gift shop at the latter will utterly ruin your diet.

KolnTriangle

"This place is temporarily closed." This skyscraper offers commanding views of the Cologne Cathedral and invites visitors to look at exhibitions, eat at its Mongolian barbecue restaurant and take in views of the surrounding area from its Panorama Observatory. Entrance to the building is free, access to the viewing platform costs 3 euros. Open Oct. 1 to April 30, Monday-Friday from noon-6 p.m.,...