If you climb the Dom, it makes it hard to see the Dom (plus the 533 steps can be a workout). We like to take our friends to the Triangle first. On top of the tower you get a full view of the city, the Rhein, and more than a little of the surrounding area.
Visiting the Triangle gives you a chance to see Cologne from way up high. Up top, they've included markers to point out what you're seeing, giving you an overview of the city instantly. On top of that, check out the area around Cologne from there (Bonn, the Seven Hills, Leverkusen), especially on a clear day!
The Triangle is one of the cheaper attractions in the city but is never too busy. Make sure you check the hours as they change from summer to winter!
Mon-Su: 11:00-18:00
Mon-Su: 11:00-23:00