You can get to Cologne easily by train with the Eurostar via Brussels and I actually recommend it, it takes less than 5 hours with about on hour changeover in Brussels, it's a much more pleasant way to travel and there are a few options during the day. You can book the ticket all the way through on the Eurostar website, if I remember well tickets go on sale 4 months in advance (I'm sure about the Eurostar, I don't honestly remember if that applies to the Brussels-Cologne leg too - if it doesn't then you can still book the whole in one go but you have to wait till 3 months in advance).
The Palladium, while not in the city centre, is fairly easy to reach by U-bahn (metro) and/or tram, and even a taxi from the city centre costs relatively little (certainly compared to London!), so I wouldn't worry about that too much.
Hope that helps
