I'm not a local to Copenhagen, but I visited two years ago. Spent a long weekend there. We rented an apartment near Tivoli Gardens.
For a one day visit, I would recommend visiting Amalienborg, Christiansborg, and sitting out at one of the restaurants at Nyhavn on a sunny day! And Tivoli in the evening. The marble church is beautiful too. We walked everywhere in Copenhagen and did not use public transport once, so I have no tips for that as a tourist!
If you have more than one day, and are happy to use public transport to venture out of the city, I loved visiting Elsinore and Hillerod more than visiting Copenhagen. Elsinore is where the castle where Hamlet was based is located (Kronborg castle) and is a quaint little town. Hillerod is home to Frederiksborg castle which is just spectacular inside. Highly would recommend either of these towns to visit! It is possible to do them both in one day as long as you schedule your day well.
For a one day visit, I would recommend visiting Amalienborg, Christiansborg, and sitting out at one of the restaurants at Nyhavn on a sunny day! And Tivoli in the evening. The marble church is beautiful too. We walked everywhere in Copenhagen and did not use public transport once, so I have no tips for that as a tourist!
If you have more than one day, and are happy to use public transport to venture out of the city, I loved visiting Elsinore and Hillerod more than visiting Copenhagen. Elsinore is where the castle where Hamlet was based is located (Kronborg castle) and is a quaint little town. Hillerod is home to Frederiksborg castle which is just spectacular inside. Highly would recommend either of these towns to visit! It is possible to do them both in one day as long as you schedule your day well.