In my opinion, Tivoli is best at night after the lights come on, so you are spot on in planning one night there. We felt very safe walking all over the city at all hours. Honestly, I felt safer in Copenhagen at night than I do walking in downtown Pittsburgh. Remember that it will be light out until very late. Take a canal cruise, shop on the Stroget, have dinner at a sidewalk cafe or just walk. Honestly, we loved just walking and taking in the city (as did our 17 year old). We were there for 2 and a half days and it wasn't enough. Copenhagen is such a beautiful city and we found everyone to be very friendly and helpful (and most speak English very well). Enjoy!