A trip to copenhagen

My trip will be for 7 days in july, 5 of them will be free to look around.
Need advice from danes, or people traveled to denmark on some manners:

Hotel - Should I search for one that close to the center, or pick the cheapest one and use the public transportation to go from the hotel to the sites?
Transportation - Should I buy the Copenhagen card for 120 hours, or buy the public transportation pass alone and tickets to sites alone?

Must see (The local version) - Advice from danes about the local gems, not advertised propertly on the internet that I should look into.

If anyone want to join me on one of the days, you welcome to add me on steam.

Thanks in advance for all the help