Day Trip from Copenhagen

I don't know the tour, so I won't comment on that, but all the places you mention are easy to visit on your own with public transport.
You can plan all public transport on www.rejseplanen.dk and if you get the Copenhagen Card, both train tickets and entrance fees except Fredensborg are covered. Just something to take into consideration.

We took an excellent tour with this company. My review of the tour is included. Cost was reasonable. Also, we have used Viator before and never been disappointed.
www.granddaytrip.dk

The tour included

Kronborg Castle in Elsinore (UNESCO World Heritage Site)

Roskilde Cathedral (UNESCO World Heritage Site)

Frederiksborg Palace in Hillerød

The Viking Ship Museum in Roskilde

The tour was excellent as was our guide Adam. Our first stop was the Roskilde Cathedral, which dated back to 12th and 13th centuries. The cathedral was the burial site for Danish Monarchs for 500 years. There were chapels that dated back to the early years of the Cathedral and others that were added centuries later. We saw many tombs in the cathedral. The cathedral survived the Reformation but lost its bishop and some of its significance. However, it is currently a UNESCO World Heritage Site.

Next, we visited the Viking Ship Museum in Roskilde. This was probably the highlight of the tour. The museum had several Viking ships that had been excavated and reassembled (most not completely). However, full scale replicas were in the nearby harbor for all to see. We were told that those replica ships did venture out to sail. The museum had exhibits explaining how the ships were built and other details. There were two basic types of ships, the fast warships and the larger cargo ships.

Frederiksborg Palace was our next stop. This palace was over 400 years old with parts of the place from the 16th Century. It is now largely an art museum. The palace is huge and we could only see so much in two hours. We probably saw less than half of the palace. The larger rooms were impressive and the art was good, but didn’t see many works from great masters.

The drive out to Roskilde, then northeast to Frederiksborg, then east to Kronborg took us through the beautiful Danish countryside. Denmark is very flat with many rural farms, most with cattle. Kronborg was a castle sited on the west side of the sound facing Sweden (at the narrowest point). The castle was there to enforce the toll fees that Denmark charged any ship entering or departing from the Baltic Sea. These fees greatly enriched the Danish state. The castle was the site of Shakespeare’s Hamlet.

The castle dates from the 15th century, but a fire in the 17th century burned most of the building, but it was rebuilt. The Swedes captured the castle and took away the valuables during a war. In its later years, the castle was used as a prison. Not much remains inside.

We just went to Kronborg and Frederiksborg . Really easy to do from Copenhagen. Purchase the 24 hour day ticket. It covers all trains, buses, public transportation. Took the S- train.
We did it like this: Osterport to Helsingor. A 10 minute walk to Kronborg Castle. After the visit there, we returned to the train station and took the train to Hillerod. The bus stop(station) is right next to the train station. Took bus 111 to the Frederiksborg Castle and Gardens. Then bus back to the train station then back to Copenhagen.
Got to see what we wanted to see instead of being rushed with a tour group.
Have a great adventure.

We recently went to Copenhagen and did both Helsingor (Kronberg), and on another day the longship museum and cathedral at Roskilde. While Helsingor was interesting (gloomy sort of day when we went - just right!) I much preferred the trip to Roskilde - of the two Roskilde is the one not to miss. We did both trips 'under our own steam' as it were by train and on foot. Buy the 24 hour ticket for rail travel, it seems to be the cheapest option. Lots of really helpful, English speaking railway company employees on hand to help you at the ticket machines.

Whatever you decide to do, have a great trip!

Ian

We have had good results with Viator, but if you can book directly with a local company, go for it.

We did the tour you are referring to and loved it.

Others haven't mentioned much on Fredensborg Palace. I like this small town, beautiful castle and gardens. The inside of the palace and private gardens are open for tours July 1st-August 6th - this year. The rest of the year you can walk the grounds and see the sculptures and lake views. The palace is on the edge of a beautiful lake- Estrum Sø - there is also a great little restaurant Skipperhuset on the royal grounds in the old Skipper's house. To find it follow Skipperalle, the Linden covered path down to the lake (just left of the Palace gate entrance) - if you're not up for a meal there is a great ice cream /coffee place Sørup Is just a little further, go left once you get to the lake edge.