Seconding Louisiana, even if it is a day trip away, it’s the most stunning museum in the world. Great store, great museum, great outdoor space, that’s 3/3.
Bang & Jensen is a nice spot for a coffee and gets lively in the evening. If you walk from the central station after checking out Tivoli (not worth the entry fee, looking from outside is enough lol) down Istedgade, you’ll pass by some cute stores, cafés, food spots and end up at Enghave Plads. If you wanna go out, Basement usually has sommmmething interesting.
Blågardsgade has a bunch of different bars, Sorte Firkant is my fav - nice staff, great taste in music, and depending on the evening some sort of performance/DJ/concert!