Dusseldorf or Cologne
 

just have one day and one night.

which city is better between the two.
I am 45.

I would say Cologne -- but knowing your age and nothing else doesn't really help. Here is a recent thread that has some info on the two (plus Bonn)
http://www.fodors.com/forums/threads...p;tid=35105392

I like cologne much better, you can take a (short) rhine river cruise and have eather lunch or dinner at one of the restaurants by the river it is a beautiful area, of course you have to see the cathedral. Enjoy your stay.

If I wanted to go to mass at the cathedral is it hard to get in ?

Going to Mass at the Cathedral is like going to Mass at any other church only here tourists as well as locals attend. When I went to a Sunday Mass, there were lots of people, but it was not difficult to find a place to sit.

Go at least 5 minutes before Mass starts and walk straight to your chosen pew.

http://tinyurl.com/2htagt
will give you more information, including Mass times.

Cologne

Cologne is a fantastic city with a bit of everything. Cologne's skyline is dominated by the magnificent gothic cathedral but the twelve romanesque churches are also landmarks. Of course, you visit the cathedral, see the ancient shrine of the three magi and the masterpieces of medieval art. Don't forget to visit the treasure chamber. See also at least one of the twelve romanesque churches - Gross St. Martin is the largest one and easy to reach. Visit the gothic city hall and enter the basement where you can explore the remnants of the Roman palace (praetorium) and a section of a 2000-year-old sewer (you can walk inside for about 200 metres). Walk through the Old Town and along the riverside and have a rustic meal with local beer (Sion and Frueh are famous breweries serving regional fare). Visit the Roman-Germanic museum with masterpieces of Roman architecture and the very bess Roman glass artifacts. Visit the Wallraff-Richartz-Museum with its collection of medieval art and/or the Museum Ludwig with a world-class collection of modern art. All these attractions are in easy walking distance around the main station.

Dusseldorf

Dusseldorf has four main attractions: The riverfront, the old town, the art district and the shopping mall. The riverfront at the Rhine is a playground of urban life, crowded with walkers, skaters and open-air restaurants day and night. The old town is among Europe's greatest entertainment districts. Full of bars and restaurants. Uerige is a microbrewery serving local beer inside and outside. Within the Old Town, you find the old harbour (with a historical Rhine ship), the renaissance city hall, two splendid baroque churches and a quite and fine gaslamp district, the Karlstadt, with fine baroque architecture. Dusseldorf is also a center of art, with two outstanding collections, K20 (20th century art) and K21 (21th century art). The MuseumKunstPalast hosts outstanding exhibitions. And Dusseldorf is home to Germany's most elegant shopping street: The Koenigsallee, an tree-lined alley along the Dussel river with most elegant shops.

Similar decision to make. Which of the two cities has more options for budget accommodation? budget = 50-60 euros a night for a single (don't mind shared bathroom).

Any thoughts or recommendations?

Thx.

Check www.hrs.de for discounted hotel rooms. Single w/ private bath should be no problem with your budget -- unless there is a major event (fair, convention, etc.) at the time you wish to travel.