Absolutely gorgeous and gives a feeling of Old Tokyo. All around the cemetery are many shrines and temples which are completely worth a visit. It's also very near the Yanaka market.
Take the ferry to Centre Island and rent a bike then head to Ward's Island (they're connected). Stop for lunch and a drink at Rectory Cafe, they even have bike parking. It's great. There's a hippie village out there and you can race kids on scooters. Fun.
I'm not even the biggest seafood eater, but I will have dinner here every time I'm in Copenhagen. If you like seafood it's a place you must visit. Must.
If you're bringing your wife, get the penthouse suite. Totally amazing and has it's own private rooftop deck (and huge puffy lounge seat for two, with a fire pit if it's cold) with a great view of the city. They also have a great scandinavian spa on site. Love the ambiance of this place.