Our flight from Toronto to Copenhagen lands at 9 am. We cannot check into our hotel until 3 pm. We will be jet lagged and sleep deprived. Any ideas on what to do during this time frame?
See if the hotel will hold your luggage until your room is available. Then take a walk and maybe a place that serves very strong coffee. That strategy has worked for us in the past.
Leave your luggage at the hotel and walk the pedestrian street Strøget. Have great hot chocolate and Danish layer cake at La Glace conditori on Skoubogade. The sugar high should keep you awake!
If you land at 9, you may not be into Copenhagen until 10:00 or 10:30 (although the Central Station is a very short and convenient train ride from the airport). As the others have suggested, I would first stop at your hotel. They will certainly hold your luggage for you, but who knows, your room might be ready early? We arrived at our hotel in Copenhagen around 11:30 a.m. or noon, and check-in time was also 3. We only intended to drop our bags off, but our room was ready so we checked in, and this has happened in other hotels/cities too. Maybe you'll get lucky.
After flying a red eye, we usually do our best to push through the day and stay awake until at least 9 or 10 p.m. that night. If you can do that, you'll sleep like a baby and then pretty much adjusted to the new time zone. I agree with the others that the best way to do this is to walk around. Avoid sitting around or getting too cozy. We often try to hit some of the more "outdoor" sites we wish to visit on that first day.
This might be a bit aggressive for some, as it involves a lot of walking, but I might consider the following for Copenhagen. Also with the caveat that I don't know how old you are and if you have physical limitations, etc., that would prevent you from walking a lot. If you plan to go, I think Christiania would be fun and a good way to stay away. It's interesting and makes for a great walk (get past Pusher Street and explore the beautiful, quieter areas and the unique houses). This isn't everyone's cup of tea, but we enjoyed it. You could get lunch at Copenhagen Street Food, which is on Papiroen, very near Christiania. There are probably 20-30 different food stalls that serve affordable meals - French, Chinese, Burgers, smorrebrod, you name it, they've got it. There are a bunch of picnic tables outside, and it's situated on the water. On a nice day, there are few places in Copenhagen I'd rather pass an hour or two. There are at least two bars in Copenhagen Street Food too, so you can grab yourself a beer and people watch.
From there, maybe walk to Nyhavn, and continue up to the Kongens Have, see the beautiful gardens, and go to Rosenborg Slot. It's a relatively small but great castle right in the city. Late in the afternoon, find a spot for a cup of coffee and a pastry, or a drink. Head back to hotel - don't lay down! - and get ready for dinner.
We just went through that scenario last week. We took the canal boat tour that RS recommends, sitting with the little mermaid and assembled audience for 30 minutes to stretch the tour out a bit. Then we found a cafe had a leisurely dinner and went to bed about 7 pm local time. Worked well. You could add the RS city walk to get some more time in the outdoors gently if you can bear to do it. The walk is easy to follow and a useful orientation. Enjoy your trip.
If you want a nice walk you can start behind Rosenborg Castle (the barracks in Gothersgade) at 11:27 when the royal guard is mustered and follow them to Amalienborg for the changing of the guards. See http://changing-guard.com/changing-guard-worldwide/copenhagen-denmark.html