I will be staying at Bethel Hotel and am looking for relatively inexpensive lunch/dinner options--any suggestions?
I wonder why you want to eat in that small area, as it's the most expensive, oppressively touristy part of the entire city.
If you're visiting during summer, go around the corner to the Ofelia Plads. There are bars, food trucks and a harborfront cafe. Or take the short walk across the Knippelsbro to the Christianshavn island, where numerous relatively affordable eateries can be found. Remember, though, that Copenhagen is expensive at best. I would avoid Freetown Christiana.
We found several eating places in the Nyhavn area that we liked on our August trip.
Cafe Oscar at Bredgade 58 - dinner reservation for a table by a window
Nyhavn 41 for dinner sitting outside by the water
Mormors Cafe at Bredgade 45 - takeout for lunch ( a great chicken club sandwich)
The food court on the top floor (5th floor) of the Magazin du Nord department store on Kongens Nytorv square for lunch
Ice cream at Isobar at Havnegade 51
The Fodex Food grocery stores have prepackaged items you could have for lunch also.
We loved Copenhagen and the walkable area around Nyhavn. Be sure to take a one hour Stromma Canal boat tour from Nyhavn. It was a highlight.
I would suggest Holberg no 19. It is right around the corner from Nyhavn but is a local’s cafe. The menu is small but the food is good and one of the cheaper options in that area.
Of course getting a classic Danish hot dog with all the toppings from a cart is always a good choice too!