We are cruising from Coopenhagen to Iceland june 2024 we plane on staying 3 days before cruise …looking for hotels near cruise port

What is your 'moderate'? An actual number would help . . .

I’m thinking 200-250 a night

There’s no need to stay by the cruise port, Copenhagen isn’t very big & the port isn’t far so the city centre would be the best place to stay.

The Admiral (quirky rooms as it’s an old warehouse)
The Square - great central location
The Alexandra if you like mid century modern, close to the Square
Skt Petri
Babette Guldsmeden
Nyhavn 71(quirky rooms like the Admiral, great location)
CPH Living if you want to stay in a floating hotel

There are many others that are great too but this might give you something to start with.

When in June, if it’s close to midsummer then hotels might be more expensive during that time.

I don’t know about its proximity to the cruise port, but we enjoyed staying at the Hotel Kong Arthur. (Front door access up too many stairs was challenging for us upon arrival with luggage. We soon discovered easier access around the corner, with short ramp and no stairs.) Spacious room, reception in the lobby each evening with one free drink, generous and tasty buffet breakfast.

thank you very much for your suggestions

I use Booking.com and search for hotels using my criteria than read the reviews and cross check the few left with TripAdvisor

Copenhagen is a wonderful small city to explore. You don’t want to stay near a cruise dock rather in the charm of the city. Look in the Nyhaven area for your hotel. One nice hotel there is The Admiral.

Has anyone stayed at the Tivoli hotel