We cruised out of Copenhagen last year and it quickly became one of my favorite cities.
Our family of three adults stayed 2 nights pre-cruise and 1 night post-cruise in 2 different hotels. Pre-cruise, we stayed at the Copenhagen Marriott, which was about a ten-minute walk to Tivoli Garden. Post-cruise was at the Hilton Copenhagen Airport. Our son had a sofabed at the Hilton; I'll have to check if it was a single or double bed. I believe he had a double bed at the Marriott. Both hotels were great and convenient to public transit. I booked both on the hotel's websites, so I was able to see the occupancy information.
I'll also have to get back to you on the cruise terminal. I did not note the terminals in my journal.