In the novel "Journey to the Center of the Earth" Jules Verne sends his protagonists to the Snæfellsnes peninsula to start their descend into the planet´s core. So far even 150 years after the book was published no local tour operator offers this activity. So it seems there are other things you will have to do rather than going down the abyss and fighting giant lizards. Other options which come close to this experience are a large variety of day tours offered by many operators. The tour into vatnshellir cave ( which is on the Snæfellsnes peninsula) is one option, where you get to go below in Iceland. If you are only doing day trip to the peninsula in the west of Iceland especially during the winter time there are other tours which are highly recommended. Especially if you are travelling around Christmas and new year s eve. The days are very short for the guests visiting Iceland in December, so we would recommend to pick a shorter day trip.
Such as the south coast day tour which takes you out to see the magnificent waterfalls Skógafoss, Seljalandsfoss as well as the city of Vik in the south. During the tour you can also from the distance see the volcano Eyjafjallajökull, which in 2010 put many flights on hold. There are no news on people trying to descent through it to see the center of the earth, but who knows, maybe the eruption was only a big cover-up.
And in between day trips you can stay in Reykjavik and see the cute little Christmas village it becomes in December. The streets in the center are brightly illuminated opposing the dark forces of winter bringing light to us. A special Idea in Reykjavik is always to go to one of the may geothermal swimming pools located in the city. Opposed to the blue lagoon they are cheaper and usually not as crowded. Few things are more relaxing than sitting in one of the hot tubs while it is freezing cold around you and see everything covered in Snow. If you want to be more active you can consider ice skating in Laugardalur, conveniently located next to the biggest swimming pool and a great Hot Dog Stand.
In downtown Reykjavik about thirty minutes walking from Laugardalur you will find the Oslo Christmas tree, beautifully positioned on Austurvöllur square outside the parliament. Decorated with Christmas lights and more.
Many winter visitors come in the hope to go ice caving which is a unique and special experience. Only problem being that most natural ice caves appear a bit too far away from Reykjavik to comfortably reach them and be back in Reykjavik in time for happy hour.
The other big winter attraction is going on a northern lights tour, which you can do after dinner. Either by boat ( with a bar) or by coach ( no bar but usually hot cocoa). These tours are no guarantee, but sure they enhance your chances to see the Aurora Borealis.
If you want to go on a boat tour and see something you can consider whale watching, the tours are operated all year, and also in winter you are able to experience the gentle giants in their natural habitat. An experience completely different from seeing their cousins in captivity perform at a water park.
For Icelanders an important tradition is going to see one of the may Christmas concerts. Most of them are held by famous Icelandic artists at Harpa concert hall. Afterwards they may go to ingólfstorg square and have a drink or two.