We will be leaving on a cruise in August and need two affordable nights in Copenhagen prior to the departure. What part of town should we be staying, and should we be close to the Freeport departure dock or does it matter.
We stayed at the Radisson Blu Royal Hotel. It is directly across from Tivoli Gardens. We could walk everywhere. Copenhagen isn't very big and you can walk or take a bus. We had a room overlooking the main street. We could watch the fireworks every night at Tivoli. Our room was high up, but right on the street. It was very soundproofed. We couldn't hear any street noise. The hotel is very close to the railroad station. Copenhagen is extremely clean. Everywhere you look, you see bicycles. During the six nights we spent at the hotel, we would eat breakfast in the hotel. The corner restaurant looked out on the bicyclists. It was comical to see all the people riding their bikes. We very much enjoyed the hotel and it location.
Copenhagen is an expensive city and a good 'affordable' hotel will be hard to find for less than about $250/night. If you are fortunate to be in Copenhagen on a weekend, many hotels will have discounts for Fri-Sun. It's not really walkable from the dock area to the main tourist sights.
There is a bus stop near the cruise ship terminal where you can get a ride to the central city. Depending on what you want to see, a hotel near Tivoli Gardens or the Nyhavn Canal will put you near places you can walk to. A good place to start looking for a hotel is tripadvisor.com. You can probably find one that suits you that's ranked in the top 30.