You can usually get the excellent Marriott hotel on priceline for 100 USD plus Danish taxes (30 or so). Thatīs my choice when in CPH. You can walk to most places and there are free bikes around if you have the needed coin to get the lock opened.

Other than that itīs not that bad. It is expensive, but plenty of budget options too. Just avoid full service restaurants and eat at fast food joints or sandwiches from markets etc. If you need cheap coffee, just buy one from 7-Eleven and sit on a square or a park. As fine as being served in a fancy hotel lobby.