My husband, myself and our twins (age 16) just returned from our Denamrk & Norway summer trip. As the RS travel forum was immensely helpful in our planning I thought I would share some notes on our trip now that we have returned for others planning a visit.
Icelandair - we flew Economy Light from BOS to KEF and then on to Copenhagen. Icelandair has many different variations in tickets, ours was the lowest option and least expensive option. I don't see the advantage of paying for a higher option with this airline.. Food is extra and must be ordered in advance of your travel, we didn't bother. Two beverages were provided. We didn't find much in the way of food options in the airport at KEF (at least early in the am) except a market type place. FYI you need to scan your boarding pass to gain entry to the market and the cashier needs it when ringing you up. We subscribe to Rick's philosphy of packing light so did not check any bags.
We stayed at the Villa Copenhagen which was lovely! The hotel is very stylish (and pricey) and we enjoyed our stay. Yes the rooms are tight but nicely furnished and very comfortable. Our room overlooked the rooftop pool & bar which is used by advanced reservation and an additional fee. The pool is not huge but the reservations help it to not be overcrowded. Those 17 and under cannot use the pool after 7 pm. The breakfast buffet is the best we had all trip. Simply amazing! Food & drink from the lobby bar was delicious too. Location for us was very convienent next to the train station and diagonal from one end of Tivoli Garden. One night we saw fireworks from TG from our hotel room.
The Copenhagen Card is 100% worth it and was handy to use from the airport to our hotel too. Note that while it provides admission to Tivoli if you want to go on any rides you will need to buy a bracelet or you can pay per ride at the entry point to each ride. Example of paying per ride bumper cars would have cost us $18 for both kids to ride once, but their credit card machine was down and the operator said "no problem" and let them on anyway. Tivoli Food Hall is a great easy option especially if you are traveling with those with varying tastes (i.e. teens!). You can enter it from outside of the park too, from the street across from the train station.
We used Rick's Copenhagen & The Best of Denmark book to aid in planning. His city walk is always a great way to get a lay of the land. Canal Tours Copenhagen was included with our Copenhagen Card, this was not the boat Rick suggests. Our particular tour narrator was so obnoxious that we couldn't wait for it to be over and we weren't the only ones which was sad because cruising the canals was lovely otherwise. The plus with CTC is there are no stops for others to get on/off and it was a totally open air boat.
Our day trip to Rosklide we took the train (20 - 30 minute ride) and walked to all the sights. The Viking Museum is a must. If you want to go out rowing on the boats you need to book that at the ticket office when you enter the complex (not in the museum). Not sure if you can book online. We went an hour after opening and they were sold out for the day. The Rosklide Cathedral was another favorite. Make sure to check the cathedral's daily calendar on their website as during the summer season they are sometimes closed for parts of the day due to services/events (this is not noted in the guidebook).
Rosenborg Castle you really need to make advance reservations for. We did not but luckily got there at opening and they were not sold out for the day and we only had to wait 30 minutes till our entry time. You will need to use their lockers (token system, no charge) as they are super strict on bag size. The castle was okay and the gardens were really underwhelming.
The emphasis on biking and walking = few cars on the road and an overall calming vibe in the city overall. Just keep aware of the bike lanes when walking!