The Römisch-Germanisches Museum

The museum with a glimpse of the Dom on the left.

The Römisch-Germanisches Museum or Roman-German Museum (RGM) is an archeological museum conveniently located next to the Dom and Schildergasse across from Cologne Main Station, so there's no excuse not to visit!

Like many other museums in Europe, students under the age of 25 who produce a students card are able to receive a discount on their admission ticket. When I visited the museum (June 2014), student admission was just over 3 euros (~$3.35). 

Cologne Cathedral (Kölner Dom)

The Dom in all its Gothic glory.

Everyone knows most major cities have iconic buildings you must visit: Taipei 101 in Taipei; the Empire State Building in New York City; the Eiffel Tower in Paris, etc. For Cologne, it's the Cologne Cathedral, also known as the Dom. 

The Dom towers over downtown. I say "towers" rather reluctantly since you can feel yourself under its shadow as if its something menacing - and it does look menacing because of it's Gothic appearance. Yet, at the same time, the Dom is a church, so perhaps "protective" would be a better way to describe it's presence. Either way, you can't miss it even if you tried. I don't know why you would avoid it. Even if you aren't an architecture buff or of religious persuasion, a short one hour stop at the Dom is worth it. A person can't even make an excuse for not visiting it since it's across the way from the main station.