Stay in Vesterbro or Amagerbro neighborhood, and Gothenburg too.

For two seniors i would say Amagerbro, but it really depends on the location within these neighborhoods. The area just behind the central station in Vesterbro is the old red light district and a bit seedy, but the further away from the station you get, the cooler it becomes, but maybe mopre for the younger crowds. Amagerbro is a bit boring in my mind, but if you stay close to Christianshavn it ads up for it. (By the way, there are no canals as such in Amagerbro). If you have a street name or adress it would be easier for me to advice.
With regards to visiting Louisiana and the castles (Wich castles are you refering to? Kronborg, Frederiksborg, Fredensborg???) I would say they are better done as one or two day trips from Copenhagen, especially since they are not at all on the way to Gothenburg via train, since the direct train to Gothenburg goes via Malmø in Sweden.

Thank you for getting back to me so quickly. The place I am considering in Amagerbro is not far from the the Badminton Club between Store Molle Vej and Amagerbrogade. One of the places I am considering in Vesterbro is not far from the Planetarium. I am not sure what is best for the three of us-two seniors and 35 year old son. We usually prefer to be in the city center to make access to sights easier. As for visiting the Louisiana etc., my thought was on the day we leave Copenhagen, we would visit it as well as Frederiksborg and Kronberg Castles. Then we we would catch the train to Malmo and switch trains to Gothenburg. Are there places to store our bags at these sights before boarding the train?

The area in Amagerbro near the badminton club is a quiet residential neighborhood, nothing particulaly speciel, but very close to Christianshavn on the other side of the old fortifications, which is a very nice area and close the the city centre. The area around the Planetarium can be a bit hit and miss (the lakes around the Planetarium are very nice, but there is a big strip club just across the street). Gl. Kongevej and Vesterbrogade quite hip, but you should avoid Istedgade near the central station, which is full of porn shops and the odd junkie. However i think this only shows how peacefull Copenhagen really is, when the dodgiest neighborhood in the city is confined to one street :-)
Visiting Kronborg (and dont forget the town of Helsingør as well, it's quite scenic), Louisianna AND Frederiksborg in one day would be stretching it a bit in my opinion, let alone continuing on to Sweden on the same day, especially for two seniors. My advice would be to see Kronborg, Helsingør and Louisisana in one day and then Frederiksborg + Sweden on another day. Use www.rejseplanen.dk to plan your travels with public transport.

Thank you so much for your feedback. I just found another apartment near the Museum of Modern Art, Rosenberg Castle, and Kings Garden in Kobehaven. Perhaps that area is a better compromise between the two. Our son would like to be where we can walk everywhere as well as close to public transportation.

You are welcome. I would go for the last apartment.

Morton, we did and thanks again.