To shop you can always go to Neumarkt, it’s a place full of street with tons of differents stores. There is another place to shop, which is close to Neumarkt but I can’t remember the name now. Things there are a bit expensive though, I’ll check that one and the name of some other streets and write you back.
I’m not sure which kind of music you like, but if you like rock as I do, you definitely must go to Rose Club (http://www.rose-club-cologne.de/) and Underground (http://www.underground-cologne.de/). Let me know which kind of party you like and I can tell you some other places. There are tons of clubs at Friesenplatz, Barbararosplatz, Zülpicherplatz and Rudolfplatz, all of them rechable by train.
The Dom is a must see, and if you are not afraid of closed spaces or heights, you can go upstairs. 500 steps to the top of the tower. Close to it there’s the Museum Ludwig (mordern art).And adjacent to the Dom you find the Römisch-Germanisches Museum, which is great if you wanna know about the romam history of the city.
Agnesviertel is a good place to go if you like bars, art galleries, bookshops… There are also some historical monuments and a flea market (every 4 weeks during the summer, I think)
They have a blind restaurant (Unsichtbar) Im Stavenhof 5-7, near Hansaring and Ebertplatz. Basically, you eat in total darkness and you really gotta try your food, smelling it, touching…
I guess you are going during the summer, so, normally people buy Kölsch (Köln’s beer) and sit by the river or stay at Heumarkt.
All the places there are really easy to reach. You can walk to most part of them, or get the tram.
Let me know if there is anything specific you would like to know. I hope you have lots of fun!
P.s.: Do not forget to visit the Schokoladenmuseum.
P.s.2: There is a theme park which is not in Cologne, but in Brühl, called Phantasialand, it’s quite close and easy to get there. (http://www.phantasialand.de/)