sorry, can't help with the restaurant thing as I never really went to dinner in Copenhagen.

Concerning Tivoli - there would not be much for me on days either, but at night it can be a lovely sight. So maybe this is a chance to stroll around after your dinner.

And for the afternoon - there are such busses in Copenhagen which are used now in many tourist towns where you can hop-on-hop-off as often as you want. That way you get around the city rather easily and can see the inner city as well as the mermaid or the Amalienborg castle e.g. Those tours stop at several places obviously but the main stop is on the north west edge of the main station iirc.

Another possibility is a boat trip which shows you different parts of the city from a lovely perspective - but you can't get off the boat if you like a place especially....

Greets, Baerbel (near Stuttgart